42 The implicit function theorem











>> YOUR LINK HERE: ___ http://youtube.com/watch?v=bk9IKHS5KbY

Calculus 2 - international • Course no. 104004 • Dr. Aviv Censor • Technion - International school of engineering","styleRuns":[{"startIndex":0,"length":107,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":107,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"messageRenderer":{"text":{"runs":[{"text":"Comments are turned off. "},{"text":"Learn more","navigationEndpoint":{"clickTrackingParams":"CNIBEJY7GAAiEwi76fmrv9yLAxWe9kIFHSkDGqE=","commandMetadata":{"webCommandMetadata":{"url":"https://support.google.com/youtube/answer/9706180?hl=en","webPageType":"WEB_PAGE_TYPE_UNKNOWN","rootVe":83769}},"urlEndpoint":{"url":"https://support.google.com/youtube/answer/9706180?hl=en"}}}]},"trackingParams":"CNIBEJY7GAAiEwi76fmrv9yLAxWe9kIFHSkDGqE="}}],"trackingParams":"CNEBELsvGAIiEwi76fmrv9yLAxWe9kIFHSkDGqE=","sectionIdentifier":"comment-item-section"}}],"trackingParams":"CNABELovIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"QjpIGJm6TLQ","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/QjpIGJm6TLQ/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AHGBIACuAOKAgwIABABGGMgZShXMA8= rs=AOn4CLCEXiK92PLQYAE9LZZTLuf8sEa7Ng","width":168,"height":94},{"url":"https://i.ytimg.com/vi/QjpIGJm6TLQ/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgBxgSAArgDigIMCAAQARhjIGUoVzAP rs=AOn4CLCrUg7M9xkfQf0oY4DH29uhlttGSg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"43 - The implicit function theorem - continued by ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ 51,459 views 9 years ago 37 minutes"}},"simpleText":"43 - The implicit function theorem - continued"},"longBylineText":{"runs":[{"text":"ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ","navigationEndpoint":{"clickTrackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@technion.israel","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4_i7cYMdM0MkP-2ywVlhKQ","canonicalBaseUrl":"/@technion.israel"}}}]},"publishedTimeText":{"simpleText":"9 years ago"},"viewCountText":{"simpleText":"51,459 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"37 minutes, 37 seconds"}},"simpleText":"37:37"},"navigationEndpoint":{"clickTrackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWRIttPkpYeF0qdumgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=QjpIGJm6TLQ","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"QjpIGJm6TLQ","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nv47zn7y.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=423a481899ba4cb4 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2965000 mt=1740405913 oweuc= pxtags=Cg4KAnR4Egg1MTM5OTk3NQ rxtags=Cg4KAnR4Egg1MTM5OTk3MQ%2CCg4KAnR4Egg1MTM5OTk3Mg%2CCg4KAnR4Egg1MTM5OTk3Mw%2CCg4KAnR4Egg1MTM5OTk3NA%2CCg4KAnR4Egg1MTM5OTk3NQ%2CCg4KAnR4Egg1MTM5OTk3Ng%2CCg4KAnR4Egg1MTM5OTk3Nw%2CCg4KAnR4Egg1MTM5OTk3OA"}}}}},"shortBylineText":{"runs":[{"text":"ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ","navigationEndpoint":{"clickTrackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@technion.israel","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4_i7cYMdM0MkP-2ywVlhKQ","canonicalBaseUrl":"/@technion.israel"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/u-MlQhgY-fSYqi8djpU9_Es4H4D4y88MfMfEsXqcjdv3IHDH89mZTNU5Ano4nc_yT4GMufJAeg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqFAtJnpzYmDkp1C","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"51K views"}},"simpleText":"51K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CM4BEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CM4BEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"QjpIGJm6TLQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CM4BEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["QjpIGJm6TLQ"],"params":"CAQ%3D"}},"videoIds":["QjpIGJm6TLQ"]}},{"clickTrackingParams":"CM4BEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CM8BELlqIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},"popupType":"TOAST"}}]}},"trackingParams":"CM4BEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CM0BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","offlineVideoEndpoint":{"videoId":"QjpIGJm6TLQ","onAddCommand":{"clickTrackingParams":"CM0BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","getDownloadActionCommand":{"videoId":"QjpIGJm6TLQ","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CM0BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqE=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtRanBJR0ptNlRMUQ%3D%3D","commands":[{"clickTrackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqE=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMwBEI5iIhMIu-n5q7_ciwMVnvZCBR0pAxqh","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqE=","hasSeparator":true}}],"trackingParams":"CMkBEKQwGAAiEwi76fmrv9yLAxWe9kIFHSkDGqE=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"37 minutes, 37 seconds"}},"simpleText":"37:37"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMsBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"QjpIGJm6TLQ","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMsBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"QjpIGJm6TLQ"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMsBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMoBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMoBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"QjpIGJm6TLQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMoBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["QjpIGJm6TLQ"],"params":"CAQ%3D"}},"videoIds":["QjpIGJm6TLQ"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMoBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"43 - The implicit function theorem - continued - 37 minutes - Go to channel - ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ - 51K views - 9 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/QjpIGJm6TLQ/mqdefault_6s.webp?du=3000 sqp=CLjU8b0G rs=AOn4CLClRsnytFQO6kETHj9sXkQgVIYd4Q","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"5A39Ht9Wcu0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/5A39Ht9Wcu0/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBgEXloS5sIOooVn-7003rIcHgP0Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/5A39Ht9Wcu0/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLATxKTjL3UZauG5l211XNyYUujRsg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Understanding Lagrange Multipliers Visually by Serpentine Integral 385,081 views 3 years ago 13 minutes, 18 seconds"}},"simpleText":"Understanding Lagrange Multipliers Visually"},"longBylineText":{"runs":[{"text":"Serpentine Integral","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SerpentineIntegral","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCo-H6EyTbD-7inMwW70QdtA","canonicalBaseUrl":"/@SerpentineIntegral"}}}]},"publishedTimeText":{"simpleText":"3 years ago"},"viewCountText":{"simpleText":"385,081 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"13 minutes, 18 seconds"}},"simpleText":"13:18"},"navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWRIttPkpYeF0qdumgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=5A39Ht9Wcu0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"5A39Ht9Wcu0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nv47zn7y.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=e40dfd1edf5672ed ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2965000 mt=1740405913 oweuc= pxtags=Cg4KAnR4Egg1MTM5OTk3NQ rxtags=Cg4KAnR4Egg1MTM5OTk3MQ%2CCg4KAnR4Egg1MTM5OTk3Mg%2CCg4KAnR4Egg1MTM5OTk3Mw%2CCg4KAnR4Egg1MTM5OTk3NA%2CCg4KAnR4Egg1MTM5OTk3NQ%2CCg4KAnR4Egg1MTM5OTk3Ng%2CCg4KAnR4Egg1MTM5OTk3Nw%2CCg4KAnR4Egg1MTM5OTk3OA"}}}}},"shortBylineText":{"runs":[{"text":"Serpentine Integral","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SerpentineIntegral","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCo-H6EyTbD-7inMwW70QdtA","canonicalBaseUrl":"/@SerpentineIntegral"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kmVQp2By-Up_8qr_5Rlny6kjWYM3S98A2MVq9hSS9gpQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqFA7eXZ-u2j_4bkAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"385K views"}},"simpleText":"385K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMcBEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMcBEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"5A39Ht9Wcu0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMcBEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["5A39Ht9Wcu0"],"params":"CAQ%3D"}},"videoIds":["5A39Ht9Wcu0"]}},{"clickTrackingParams":"CMcBEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMgBELlqIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},"popupType":"TOAST"}}]}},"trackingParams":"CMcBEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CMYBENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","offlineVideoEndpoint":{"videoId":"5A39Ht9Wcu0","onAddCommand":{"clickTrackingParams":"CMYBENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","getDownloadActionCommand":{"videoId":"5A39Ht9Wcu0","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CMYBENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqE=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs1QTM5SHQ5V2N1MA%3D%3D","commands":[{"clickTrackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqE=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMUBEI5iIhMIu-n5q7_ciwMVnvZCBR0pAxqh","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqE=","hasSeparator":true}}],"trackingParams":"CMIBEKQwGAEiEwi76fmrv9yLAxWe9kIFHSkDGqE=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"13 minutes, 18 seconds"}},"simpleText":"13:18"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"5A39Ht9Wcu0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"5A39Ht9Wcu0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMQBEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMMBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"5A39Ht9Wcu0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["5A39Ht9Wcu0"],"params":"CAQ%3D"}},"videoIds":["5A39Ht9Wcu0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMMBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Understanding Lagrange Multipliers Visually - 13 minutes, 18 seconds - Go to channel - Serpentine Integral - 385K views - 3 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/5A39Ht9Wcu0/mqdefault_6s.webp?du=3000 sqp=CODx8b0G rs=AOn4CLDsT5CDtb7Gd_6-ZSiOBsUXdFVBUQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"UYSwBx38cpQ","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/UYSwBx38cpQ/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AHGBIACuAOKAgwIABABGGQgZShZMA8= rs=AOn4CLCyemKp1AtT1dX5OM-L0J20KarjQA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/UYSwBx38cpQ/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgBxgSAArgDigIMCAAQARhkIGUoWTAP rs=AOn4CLDmPTrnOmxpA8W9ZI2nbn031hfBcg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"44 - Proof of the implicit function theorem by ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ 43,044 views 9 years ago 21 minutes"}},"simpleText":"44 - Proof of the implicit function theorem"},"longBylineText":{"runs":[{"text":"ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ","navigationEndpoint":{"clickTrackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@technion.israel","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4_i7cYMdM0MkP-2ywVlhKQ","canonicalBaseUrl":"/@technion.israel"}}}]},"publishedTimeText":{"simpleText":"9 years ago"},"viewCountText":{"simpleText":"43,044 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"21 minutes, 7 seconds"}},"simpleText":"21:07"},"navigationEndpoint":{"clickTrackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWRIttPkpYeF0qdumgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=UYSwBx38cpQ","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"UYSwBx38cpQ","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=5184b0071dfc7294 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1296250 mt=1740405913 oweuc= pxtags=Cg4KAnR4Egg1MTM5OTk3NQ rxtags=Cg4KAnR4Egg1MTM5OTk3MQ%2CCg4KAnR4Egg1MTM5OTk3Mg%2CCg4KAnR4Egg1MTM5OTk3Mw%2CCg4KAnR4Egg1MTM5OTk3NA%2CCg4KAnR4Egg1MTM5OTk3NQ%2CCg4KAnR4Egg1MTM5OTk3Ng%2CCg4KAnR4Egg1MTM5OTk3Nw%2CCg4KAnR4Egg1MTM5OTk3OA"}}}}},"shortBylineText":{"runs":[{"text":"ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ","navigationEndpoint":{"clickTrackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqEyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@technion.israel","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4_i7cYMdM0MkP-2ywVlhKQ","canonicalBaseUrl":"/@technion.israel"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/u-MlQhgY-fSYqi8djpU9_Es4H4D4y88MfMfEsXqcjdv3IHDH89mZTNU5Ano4nc_yT4GMufJAeg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqFAlOXx7_GArMJR","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"43K views"}},"simpleText":"43K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMABEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMABEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"UYSwBx38cpQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMABEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["UYSwBx38cpQ"],"params":"CAQ%3D"}},"videoIds":["UYSwBx38cpQ"]}},{"clickTrackingParams":"CMABEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMEBELlqIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},"popupType":"TOAST"}}]}},"trackingParams":"CMABEP6YBBgGIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CL8BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","offlineVideoEndpoint":{"videoId":"UYSwBx38cpQ","onAddCommand":{"clickTrackingParams":"CL8BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh","getDownloadActionCommand":{"videoId":"UYSwBx38cpQ","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CL8BENGqBRgHIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqE=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtVWVN3QngzOGNwUQ%3D%3D","commands":[{"clickTrackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqE=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CL4BEI5iIhMIu-n5q7_ciwMVnvZCBR0pAxqh","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqE=","hasSeparator":true}}],"trackingParams":"CLsBEKQwGAIiEwi76fmrv9yLAxWe9kIFHSkDGqE=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"21 minutes, 7 seconds"}},"simpleText":"21:07"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL0BEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"UYSwBx38cpQ","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CL0BEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"UYSwBx38cpQ"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL0BEPnnAxgBIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLwBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLwBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"UYSwBx38cpQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLwBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["UYSwBx38cpQ"],"params":"CAQ%3D"}},"videoIds":["UYSwBx38cpQ"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLwBEMfsBBgCIhMIu-n5q7_ciwMVnvZCBR0pAxqh"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"44 - Proof of the implicit function theorem - 21 minutes - Go to channel - ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ - 43K views - 9 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/UYSwBx38cpQ/mqdefault_6s.webp?du=3000 sqp=CIC98b0G rs=AOn4CLClEgJohBYaT7ID3X3Vq5j9ECncIg","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/oV0INtZT_n0/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLBXwdaVbmZ-Wiq05pMh_DaB8qQVGA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/oV0INtZT_n0/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLAPKLMfoE_lZ80udSOeT1brLtgTQg","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"100 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":2630944,"darkTheme":2630944}}}],"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":4143666,"darkTheme":4143666}}},"stackColor":{"lightTheme":12562583,"darkTheme":9208176}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Differential and Integral Calculus 2"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"ื”ื˜ื›ื ื™ื•ืŸ - ืžื›ื•ืŸ ื˜ื›ื ื•ืœื•ื’ื™ ืœื™ืฉืจืืœ

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









Content Report
Youtor.org / YTube video Downloader ยฉ 2025

created by www.youtor.org