Word problem using related rates and chain rule
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=GlYsZ76D3NA
See www.midnighttutor.com for all the latest calculus tutorial videos. Tutorial of how to solve a word problem involving price changes and rate of change of revenue.","styleRuns":[{"startIndex":0,"length":166,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":166,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CM8BELsvGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0dsWXNaNzZEM05BGAYyJSIRIgtHbFlzWjc2RDNOQTAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CM8BELsvGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CM4BELovIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"gxqSytYF66M","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/gxqSytYF66M/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLC7kZ6I9GS1LOAR1TXRzoWgYGEX-A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/gxqSytYF66M/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBrT_tSjqmHsqVVProoB4Ypi7_BkA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Chain rule word problem by Nicholas Patey 9,980 views 10 years ago 8 minutes, 56 seconds"}},"simpleText":"Chain rule word problem"},"longBylineText":{"runs":[{"text":"Nicholas Patey","navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@NicholasPatey","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCfOIzis1RwY1pqQhz6OMkEg","canonicalBaseUrl":"/@NicholasPatey"}}}]},"publishedTimeText":{"simpleText":"10 years ago"},"viewCountText":{"simpleText":"9,980 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"8 minutes, 56 seconds"}},"simpleText":"8:56"},"navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWRI0LmP9PuMi6samgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=gxqSytYF66M","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"gxqSytYF66M","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nv47zne7.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=831a92cad605eba3 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1543750 mt=1739919426 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Nicholas Patey","navigationEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@NicholasPatey","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCfOIzis1RwY1pqQhz6OMkEg","canonicalBaseUrl":"/@NicholasPatey"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_l_LCTq-WAZIvh5nPCG65sGHPkK2ygFqqDme4-2dqmUK7U=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrhAo9eXsK3ZpI2DAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"9.9K views"}},"simpleText":"9.9K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMwBEP6YBBgFIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMwBEP6YBBgFIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gxqSytYF66M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMwBEP6YBBgFIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gxqSytYF66M"],"params":"CAQ%3D"}},"videoIds":["gxqSytYF66M"]}},{"clickTrackingParams":"CMwBEP6YBBgFIhMIitTSi6rOiwMVWFp6BR1pCQa4","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CM0BELlqIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},"popupType":"TOAST"}}]}},"trackingParams":"CMwBEP6YBBgFIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtneHFTeXRZRjY2TQ%3D%3D","commands":[{"clickTrackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMsBEI5iIhMIitTSi6rOiwMVWFp6BR1pCQa4","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","hasSeparator":true}}],"trackingParams":"CMgBEKQwGAAiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"8 minutes, 56 seconds"}},"simpleText":"8:56"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMoBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"gxqSytYF66M","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMoBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"gxqSytYF66M"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMoBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMkBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMkBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gxqSytYF66M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMkBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gxqSytYF66M"],"params":"CAQ%3D"}},"videoIds":["gxqSytYF66M"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMkBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Chain rule word problem - 8 minutes, 56 seconds - Go to channel - Nicholas Patey - 9.9K views - 10 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"lpQtIOKoTPg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/lpQtIOKoTPg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBYhaypN9akcTB2vK1CjqeU1SHcJA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/lpQtIOKoTPg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAwCpUjVKH3S7lkB3NoKWybXob-IA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Step-by-Step Procedure for Solving Derivative Word Problems by Functions Calculus by Professor Calculish 12,145 views 2 years ago 13 minutes, 16 seconds"}},"simpleText":"Step-by-Step Procedure for Solving Derivative Word Problems"},"longBylineText":{"runs":[{"text":"Functions Calculus by Professor Calculish","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@professorcalculish","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC66FfSspa34_u-2ifd1gISA","canonicalBaseUrl":"/@professorcalculish"}}}]},"publishedTimeText":{"simpleText":"2 years ago"},"viewCountText":{"simpleText":"12,145 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"13 minutes, 16 seconds"}},"simpleText":"13:16"},"navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWRI0LmP9PuMi6samgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=lpQtIOKoTPg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"lpQtIOKoTPg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nv47znee.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=96942d20e2a84cf8 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1543750 mt=1739919426 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Functions Calculus by Professor Calculish","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@professorcalculish","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC66FfSspa34_u-2ifd1gISA","canonicalBaseUrl":"/@professorcalculish"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/eyenEmUk03UhGtXbYVY_dSeFLEdBNsbpoOM_X4TLfBRklEGqzZ0maTk6ujkWXjOVRORP3SpQzJY=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrhA-JmhlY6ki8qWAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"12K views"}},"simpleText":"12K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMYBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lpQtIOKoTPg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lpQtIOKoTPg"],"params":"CAQ%3D"}},"videoIds":["lpQtIOKoTPg"]}},{"clickTrackingParams":"CMYBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMcBELlqIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},"popupType":"TOAST"}}]}},"trackingParams":"CMYBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtscFF0SU9Lb1RQZw%3D%3D","commands":[{"clickTrackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMUBEI5iIhMIitTSi6rOiwMVWFp6BR1pCQa4","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","hasSeparator":true}}],"trackingParams":"CMIBEKQwGAEiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"13 minutes, 16 seconds"}},"simpleText":"13:16"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"lpQtIOKoTPg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"lpQtIOKoTPg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMQBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMMBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lpQtIOKoTPg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lpQtIOKoTPg"],"params":"CAQ%3D"}},"videoIds":["lpQtIOKoTPg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMMBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Step-by-Step Procedure for Solving Derivative Word Problems - 13 minutes, 16 seconds - Go to channel - Functions Calculus by Professor Calculish - 12K views - 2 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/lpQtIOKoTPg/mqdefault_6s.webp?du=3000 sqp=COCg1L0G rs=AOn4CLAwtIMUfaj3yHrsGIAcxBxsOKd7uA","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"9SJ-YOa4RP4","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/9SJ-YOa4RP4/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLD8RbeD3bdhHp4OdkjZXRsxAbQo5w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/9SJ-YOa4RP4/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBKt9zd6nTTC6fazmL8idJGe_h6Jg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Related Rates: Circle Problem (Dr. April Ström) by Online EdVantage 4,324 views 4 years ago 8 minutes, 37 seconds"}},"simpleText":"Related Rates: Circle Problem (Dr. April Ström)"},"longBylineText":{"runs":[{"text":"Online EdVantage","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@onlineedvantage3132","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQlCHOjoCELipPSjLwOF1Tg","canonicalBaseUrl":"/@onlineedvantage3132"}}}]},"publishedTimeText":{"simpleText":"4 years ago"},"viewCountText":{"simpleText":"4,324 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"8 minutes, 37 seconds"}},"simpleText":"8:37"},"navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWRI0LmP9PuMi6samgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=9SJ-YOa4RP4","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"9SJ-YOa4RP4","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---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=f5227e60e6b844fe ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1023750 mt=1739919426 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Online EdVantage","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@onlineedvantage3132","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQlCHOjoCELipPSjLwOF1Tg","canonicalBaseUrl":"/@onlineedvantage3132"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_k0ds6GStabRheTRdPunj1dgus5bcx8nWQTPdlYouYiSg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrhA_onhtY7Mn5H1AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"4.3K views"}},"simpleText":"4.3K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMABEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMABEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"9SJ-YOa4RP4","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMABEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["9SJ-YOa4RP4"],"params":"CAQ%3D"}},"videoIds":["9SJ-YOa4RP4"]}},{"clickTrackingParams":"CMABEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMEBELlqIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},"popupType":"TOAST"}}]}},"trackingParams":"CMABEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs5U0otWU9hNFJQNA%3D%3D","commands":[{"clickTrackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CL8BEI5iIhMIitTSi6rOiwMVWFp6BR1pCQa4","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","hasSeparator":true}}],"trackingParams":"CLwBEKQwGAIiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"8 minutes, 37 seconds"}},"simpleText":"8:37"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"9SJ-YOa4RP4","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"9SJ-YOa4RP4"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL4BEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL0BEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"9SJ-YOa4RP4","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["9SJ-YOa4RP4"],"params":"CAQ%3D"}},"videoIds":["9SJ-YOa4RP4"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL0BEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Related Rates: Circle Problem (Dr. April Ström) - 8 minutes, 37 seconds - Go to channel - Online EdVantage - 4.3K views - 4 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/9SJ-YOa4RP4/mqdefault_6s.webp?du=3000 sqp=CIqb1L0G rs=AOn4CLCeboP4kkt2IJsA5zx3k9TskV0Ofw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"gBHIZlF0TX8","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/gBHIZlF0TX8/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCZUIb_S7LZeg3wZxlb-E1tlG_d8A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/gBHIZlF0TX8/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBJmtRkxQybSbUycRyUiFG0gwD3wg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"How to Solve ANY Related Rates Problem [Calc 1] by STEM Support 90,097 views 1 year ago 18 minutes"}},"simpleText":"How to Solve ANY Related Rates Problem [Calc 1]"},"longBylineText":{"runs":[{"text":"STEM Support","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@stemsupport3645","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCAMTCW8gfx9TGKXxNqmQiXQ","canonicalBaseUrl":"/@stemsupport3645"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"90,097 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"18 minutes, 29 seconds"}},"simpleText":"18:29"},"navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWRI0LmP9PuMi6samgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=gBHIZlF0TX8","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"gBHIZlF0TX8","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---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=8011c86651744d7f ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1023750 mt=1739919426 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"STEM Support","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@stemsupport3645","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCAMTCW8gfx9TGKXxNqmQiXQ","canonicalBaseUrl":"/@stemsupport3645"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kX5EezszoIqXBfTrxQdvbS3iz28P6FOu0LES_SG70Narg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrhA_5rRi-WM8oiAAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"90K views"}},"simpleText":"90K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLoBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLoBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gBHIZlF0TX8","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLoBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gBHIZlF0TX8"],"params":"CAQ%3D"}},"videoIds":["gBHIZlF0TX8"]}},{"clickTrackingParams":"CLoBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLsBELlqIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},"popupType":"TOAST"}}]}},"trackingParams":"CLoBEP6YBBgGIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtnQkhJWmxGMFRYOA%3D%3D","commands":[{"clickTrackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLkBEI5iIhMIitTSi6rOiwMVWFp6BR1pCQa4","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","hasSeparator":true}}],"trackingParams":"CLYBEKQwGAMiEwiK1NKLqs6LAxVYWnoFHWkJBrg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"18 minutes, 29 seconds"}},"simpleText":"18:29"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"gBHIZlF0TX8","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"gBHIZlF0TX8"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLgBEPnnAxgBIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLcBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLcBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"gBHIZlF0TX8","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLcBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["gBHIZlF0TX8"],"params":"CAQ%3D"}},"videoIds":["gBHIZlF0TX8"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLcBEMfsBBgCIhMIitTSi6rOiwMVWFp6BR1pCQa4"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"How to Solve ANY Related Rates Problem [Calc 1] - 18 minutes - Go to channel - STEM Support - 90K views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/gBHIZlF0TX8/mqdefault_6s.webp?du=3000 sqp=CK2a1L0G rs=AOn4CLC_fH_RU7WxztFjtr-ny4iuYGl-qg","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/cUMvwG7wvzM/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLBfJ8wF_Rw6k7K61bVHpcwBggQR1A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/cUMvwG7wvzM/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLAR4kDbMY-krYXj73NZG4TACST6JQ","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"7 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":796175,"darkTheme":796175}}}],"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":1326873,"darkTheme":1326873}}},"stackColor":{"lightTheme":7051632,"darkTheme":7375987}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Calc 1"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"STEM Support
#############################
