Differentiating natural logarithms











>> YOUR LINK HERE: ___ http://youtube.com/watch?v=aRhHj_j0zqo

This lesson was designed to support the Cambridge International IGCSE Additional Mathematics (0606) syllabus.","styleRuns":[{"startIndex":0,"length":109,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":109,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CLIBELsvGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC2FSaEhqX2owenFvGAYyJSIRIgthUmhIal9qMHpxbzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CLIBELsvGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CLEBELovIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"yzgh8MN6yV0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/yzgh8MN6yV0/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLDqtMXSBXGCBLiEGaigO1CpHmRY6g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/yzgh8MN6yV0/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLDpO8BGtBwJ6rC-QAIKS4_WStGZBQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Differentiating natural logarithms with product and quotient rule by The Math Man 134 views 1 year ago 4 minutes, 11 seconds"}},"simpleText":"Differentiating natural logarithms with product and quotient rule"},"longBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"134 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"4 minutes, 11 seconds"}},"simpleText":"4:11"},"navigationEndpoint":{"clickTrackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=yzgh8MN6yV0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"yzgh8MN6yV0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=cb3821f0c37ac95d ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1287500 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/4FOgmP1tAdCNCCRes5njGCnxphGEpyiVC5KKxJ9-cdirnU84qbDRqylJkk_9tCo9mxULYpTa6A=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5ZA3ZLrm4y-iJzLAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"134 views"}},"simpleText":"134 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CK8BEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CK8BEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"yzgh8MN6yV0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CK8BEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["yzgh8MN6yV0"],"params":"CAQ%3D"}},"videoIds":["yzgh8MN6yV0"]}},{"clickTrackingParams":"CK8BEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLABELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CK8BEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt5emdoOE1ONnlWMA%3D%3D","commands":[{"clickTrackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CK4BEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CKsBEKQwGAAiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"4 minutes, 11 seconds"}},"simpleText":"4:11"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CK0BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"yzgh8MN6yV0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CK0BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"yzgh8MN6yV0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CK0BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKwBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKwBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"yzgh8MN6yV0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKwBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["yzgh8MN6yV0"],"params":"CAQ%3D"}},"videoIds":["yzgh8MN6yV0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKwBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Differentiating natural logarithms with product and quotient rule - 4 minutes, 11 seconds - Go to channel - The Math Man - 134 views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"lcFMcohMcVQ","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/lcFMcohMcVQ/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCZ6lFlvDO8UKeQpynOkbV9VryvjQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/lcFMcohMcVQ/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDlmE3X7UrQcwNbGXVp0WU-BES3mQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Mathematics Mock Interview, University of Cambridge by Mathematics at Cambridge 192,899 views 1 year ago 22 minutes"}},"simpleText":"Mathematics Mock Interview, University of Cambridge"},"longBylineText":{"runs":[{"text":"Mathematics at Cambridge","navigationEndpoint":{"clickTrackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathematicsatCambridge","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKCsvwBlRaRIj1onPScDKig","canonicalBaseUrl":"/@MathematicsatCambridge"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"192,899 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"22 minutes, 28 seconds"}},"simpleText":"22:28"},"navigationEndpoint":{"clickTrackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=lcFMcohMcVQ","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"lcFMcohMcVQ","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=95c14c72884c7154 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1287500 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Mathematics at Cambridge","navigationEndpoint":{"clickTrackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathematicsatCambridge","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKCsvwBlRaRIj1onPScDKig","canonicalBaseUrl":"/@MathematicsatCambridge"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nZ9oymNLTVdVUjwA-dP-YC8dHje2uZin2A452Bm298HQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5ZA1OKxwqiO0-CVAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"192K views"}},"simpleText":"192K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKkBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKkBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lcFMcohMcVQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKkBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lcFMcohMcVQ"],"params":"CAQ%3D"}},"videoIds":["lcFMcohMcVQ"]}},{"clickTrackingParams":"CKkBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKoBELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CKkBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtsY0ZNY29oTWNWUQ%3D%3D","commands":[{"clickTrackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKgBEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CKUBEKQwGAEiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"22 minutes, 28 seconds"}},"simpleText":"22:28"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKcBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"lcFMcohMcVQ","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKcBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"lcFMcohMcVQ"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKcBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKYBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKYBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lcFMcohMcVQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKYBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lcFMcohMcVQ"],"params":"CAQ%3D"}},"videoIds":["lcFMcohMcVQ"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKYBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Mathematics Mock Interview, University of Cambridge - 22 minutes - Go to channel - Mathematics at Cambridge - 192K views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/lcFMcohMcVQ/mqdefault_6s.webp?du=3000 sqp=CJCHnb4G rs=AOn4CLBn04aqc_k1x5JumVUVZkuX25ytMw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"nZANuBa5DVA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/nZANuBa5DVA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCWi9NTjLCY-lcy6r8jutC89CmiyA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/nZANuBa5DVA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAQZ4mDhInuRiyYAie4yO2CPGDTZg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"P3. Logarithms (Pure Mathematics 3 - Cambridge International A-Level) by Maths with David 1,734 views 7 years ago 4 minutes, 29 seconds"}},"simpleText":"P3. Logarithms (Pure Mathematics 3 - Cambridge International A-Level)"},"longBylineText":{"runs":[{"text":"Maths with David","navigationEndpoint":{"clickTrackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@mathswithdavid826","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCMCmlkFMptbTrA65hYCmezQ","canonicalBaseUrl":"/@mathswithdavid826"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"1,734 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"4 minutes, 29 seconds"}},"simpleText":"4:29"},"navigationEndpoint":{"clickTrackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=nZANuBa5DVA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"nZANuBa5DVA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-nvm-cxb6.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=9d900db816b90d50 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=905000 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Maths with David","navigationEndpoint":{"clickTrackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@mathswithdavid826","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCMCmlkFMptbTrA65hYCmezQ","canonicalBaseUrl":"/@mathswithdavid826"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nW6A_NjnICXTN9pMkKEzC6itWq-LXuBgSLOxOV3XnmVg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5ZA0JrktYG3g8idAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"1.7K views"}},"simpleText":"1.7K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKMBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKMBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"nZANuBa5DVA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKMBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["nZANuBa5DVA"],"params":"CAQ%3D"}},"videoIds":["nZANuBa5DVA"]}},{"clickTrackingParams":"CKMBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKQBELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CKMBEP6YBBgGIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtuWkFOdUJhNURWQQ%3D%3D","commands":[{"clickTrackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKIBEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CJ8BEKQwGAIiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"4 minutes, 29 seconds"}},"simpleText":"4:29"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKEBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"nZANuBa5DVA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKEBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"nZANuBa5DVA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKEBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKABEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKABEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"nZANuBa5DVA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKABEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["nZANuBa5DVA"],"params":"CAQ%3D"}},"videoIds":["nZANuBa5DVA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKABEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"P3. Logarithms (Pure Mathematics 3 - Cambridge International A-Level) - 4 minutes, 29 seconds - Go to channel - Maths with David - 1.7K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/nZANuBa5DVA/mqdefault_6s.webp?du=3000 sqp=CLDunL4G rs=AOn4CLAJwYMfgsvoboZyRA3GDkDEeCNAyw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"96_y7uY4UZg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/96_y7uY4UZg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDTuTKugImXarTozKoNudznCdv4Tg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/96_y7uY4UZg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLA8icGFB4P24fsVRFiTlBqoutpmtQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Italy l can you solve?? l Hardest Olympiad Math Problem by Math Master TV 239 views 3 hours ago 12 minutes, 41 seconds"}},"simpleText":"Italy l can you solve?? l Hardest Olympiad Math Problem"},"longBylineText":{"runs":[{"text":"Math Master TV","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@haiderlughmani","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCpydzgyyDKeLRfkmQl_tT7Q","canonicalBaseUrl":"/@haiderlughmani"}}}]},"publishedTimeText":{"simpleText":"3 hours ago"},"viewCountText":{"simpleText":"239 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"12 minutes, 41 seconds"}},"simpleText":"12:41"},"navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=96_y7uY4UZg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"96_y7uY4UZg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=f7aff2eee6385198 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=655000 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Math Master TV","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@haiderlughmani","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCpydzgyyDKeLRfkmQl_tT7Q","canonicalBaseUrl":"/@haiderlughmani"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_SIMPLE","label":"New","trackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5Y="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/aZk0ss63x_lgy_9Egw1QKaXTm2csoK6DyB4aKiZJaYHyixhAFR4sBUBKf0pZYjbYs7Oze4rw=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5ZAmKPhse7d_Nf3AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"239 views"}},"simpleText":"239 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJ0BEP6YBBgHIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJ0BEP6YBBgHIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"96_y7uY4UZg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJ0BEP6YBBgHIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["96_y7uY4UZg"],"params":"CAQ%3D"}},"videoIds":["96_y7uY4UZg"]}},{"clickTrackingParams":"CJ0BEP6YBBgHIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJ4BELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CJ0BEP6YBBgHIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs5Nl95N3VZNFVaZw%3D%3D","commands":[{"clickTrackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJwBEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CJkBEKQwGAMiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"12 minutes, 41 seconds"}},"simpleText":"12:41"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"96_y7uY4UZg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"96_y7uY4UZg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJsBEPnnAxgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJoBEMfsBBgDIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJoBEMfsBBgDIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"96_y7uY4UZg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJoBEMfsBBgDIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["96_y7uY4UZg"],"params":"CAQ%3D"}},"videoIds":["96_y7uY4UZg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJoBEMfsBBgDIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Italy l can you solve?? l Hardest Olympiad Math Problem - 12 minutes, 41 seconds - Go to channel - Math Master TV - 239 views - 3 hours ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/96_y7uY4UZg/mqdefault_6s.webp?du=3000 sqp=COj9nL4G rs=AOn4CLBY_AvqJg7O-p2oiR41VQtywGJo6g","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"5csnCv6zGJE","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/5csnCv6zGJE/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDDgFP1NBfzIiS0lL_ZFrlnV2ZHtA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/5csnCv6zGJE/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBUTZDLNsSW_v9_L60pzJLwR7lKwQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"What is a Function? by Mathster of Science 2,850 views 1 year ago 12 minutes, 36 seconds"}},"simpleText":"What is a Function?"},"longBylineText":{"runs":[{"text":"Mathster of Science","navigationEndpoint":{"clickTrackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathsterofScience","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCLTBD-k8riPFT-ZUbCX86EQ","canonicalBaseUrl":"/@MathsterofScience"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"2,850 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"12 minutes, 36 seconds"}},"simpleText":"12:36"},"navigationEndpoint":{"clickTrackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=5csnCv6zGJE","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"5csnCv6zGJE","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=e5cb270afeb31891 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1287500 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Mathster of Science","navigationEndpoint":{"clickTrackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathsterofScience","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCLTBD-k8riPFT-ZUbCX86EQ","canonicalBaseUrl":"/@MathsterofScience"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/CecH-ZiC4zqGYL3rC9v7WYJ-IWR6I62F2_ZvE6o_B7lqzEn5VPkDbN7i2iGoMCkHqMXwSsG6MQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5ZAkbHM9a_hyeXlAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"2.8K views"}},"simpleText":"2.8K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJcBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJcBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"5csnCv6zGJE","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJcBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["5csnCv6zGJE"],"params":"CAQ%3D"}},"videoIds":["5csnCv6zGJE"]}},{"clickTrackingParams":"CJcBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJgBELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CJcBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs1Y3NuQ3Y2ekdKRQ%3D%3D","commands":[{"clickTrackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJYBEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CJMBEKQwGAQiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"12 minutes, 36 seconds"}},"simpleText":"12:36"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJUBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"5csnCv6zGJE","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJUBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"5csnCv6zGJE"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJUBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJQBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJQBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"5csnCv6zGJE","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJQBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["5csnCv6zGJE"],"params":"CAQ%3D"}},"videoIds":["5csnCv6zGJE"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJQBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"What is a Function? - 12 minutes, 36 seconds - Go to channel - Mathster of Science - 2.8K views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"bNwXElzowCo","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/bNwXElzowCo/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLAiNkH1d_ib9lSDka2jgcVDh-EEYw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/bNwXElzowCo/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBTIANVn4BnkIEQ8bC_nCx0l-3tag","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"When does a function have an inverse? by The Math Man 462 views 9 months ago 13 minutes, 4 seconds"}},"simpleText":"When does a function have an inverse?"},"longBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"publishedTimeText":{"simpleText":"9 months ago"},"viewCountText":{"simpleText":"462 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"13 minutes, 4 seconds"}},"simpleText":"13:04"},"navigationEndpoint":{"clickTrackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=bNwXElzowCo","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"bNwXElzowCo","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=6cdc17125ce8c02a ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=655000 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/4FOgmP1tAdCNCCRes5njGCnxphGEpyiVC5KKxJ9-cdirnU84qbDRqylJkk_9tCo9mxULYpTa6A=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5ZAqoCj56Xihe5s","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"462 views"}},"simpleText":"462 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJEBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJEBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"bNwXElzowCo","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJEBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["bNwXElzowCo"],"params":"CAQ%3D"}},"videoIds":["bNwXElzowCo"]}},{"clickTrackingParams":"CJEBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJIBELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CJEBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtiTndYRWx6b3dDbw%3D%3D","commands":[{"clickTrackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJABEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CI0BEKQwGAUiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"13 minutes, 4 seconds"}},"simpleText":"13:04"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CI8BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"bNwXElzowCo","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CI8BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"bNwXElzowCo"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CI8BEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CI4BEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CI4BEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"bNwXElzowCo","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CI4BEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["bNwXElzowCo"],"params":"CAQ%3D"}},"videoIds":["bNwXElzowCo"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CI4BEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"When does a function have an inverse? - 13 minutes, 4 seconds - Go to channel - The Math Man - 462 views - 9 months ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"Ap68xepm11c","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/Ap68xepm11c/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AHUBoAC4AOKAgwIABABGGUgZShlMA8= rs=AOn4CLB47SpmrkSlZDcGHh_qK5jlSv0pcg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/Ap68xepm11c/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB1AaAAuADigIMCAAQARhlIGUoZTAP rs=AOn4CLAli2KE9B_hBEU869SXsqLA7syyeA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Quadratic equations with indices by The Math Man 4,195 views 3 years ago 3 minutes, 46 seconds"}},"simpleText":"Quadratic equations with indices"},"longBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"publishedTimeText":{"simpleText":"3 years ago"},"viewCountText":{"simpleText":"4,195 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"3 minutes, 46 seconds"}},"simpleText":"3:46"},"navigationEndpoint":{"clickTrackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWRIqp3Tx__xkYxpmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=Ap68xepm11c","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"Ap68xepm11c","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-nvm-cxb6.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=029ebcc5ea66d757 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=905000 mt=1741113912 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"The Math Man","navigationEndpoint":{"clickTrackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5YyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@themathmanYT","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UClBhsVXiw2TuiVz-kpIPSiA","canonicalBaseUrl":"/@themathmanYT"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/4FOgmP1tAdCNCCRes5njGCnxphGEpyiVC5KKxJ9-cdirnU84qbDRqylJkk_9tCo9mxULYpTa6A=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5ZA166b096Yr88C","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"4.1K views"}},"simpleText":"4.1K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CIsBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIsBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"Ap68xepm11c","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIsBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["Ap68xepm11c"],"params":"CAQ%3D"}},"videoIds":["Ap68xepm11c"]}},{"clickTrackingParams":"CIsBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CIwBELlqIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},"popupType":"TOAST"}}]}},"trackingParams":"CIsBEP6YBBgFIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtBcDY4eGVwbTExYw%3D%3D","commands":[{"clickTrackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CIoBEI5iIhMIxYuQkIzxiwMVxVZPBB1VLSOW","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","hasSeparator":true}}],"trackingParams":"CIcBEKQwGAYiEwjFi5CQjPGLAxXFVk8EHVUtI5Y=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"3 minutes, 46 seconds"}},"simpleText":"3:46"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIkBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"Ap68xepm11c","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CIkBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"Ap68xepm11c"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIkBEPnnAxgBIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIgBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIgBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"Ap68xepm11c","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIgBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["Ap68xepm11c"],"params":"CAQ%3D"}},"videoIds":["Ap68xepm11c"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIgBEMfsBBgCIhMIxYuQkIzxiwMVxVZPBB1VLSOW"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Quadratic equations with indices - 3 minutes, 46 seconds - Go to channel - The Math Man - 4.1K views - 3 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/flZ_NHjplJ4/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLCFdDGzOET5Qo9k1Fawa2xrl-R8Vg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/flZ_NHjplJ4/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLC281zjBmf61lmqAAgwZ3sRijX0RQ","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"6 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"May/June 2024 Past Papers"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"The Math Man

#############################









Content Report
Youtor.org / YTube video Downloader © 2025

created by www.youtor.org