{"id":5135,"date":"2021-09-08T20:41:13","date_gmt":"2021-09-08T15:11:13","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5135"},"modified":"2021-11-22T20:59:39","modified_gmt":"2021-11-22T15:29:39","slug":"differentiation-of-infinite-series","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/","title":{"rendered":"Differentiation of Infinite Series Class 12"},"content":{"rendered":"

Here you will learn what is differentiation of infinite series class 12 with examples.<\/p>\n

Let’s begin –<\/p>\n

Differentiation of Infinite Series<\/h2>\n

Sometimes the value of y is given as an infinite series and we are asked to find \\(dy\\over dx\\). In such cases we use the fact that if a term is deleted from a infinite series, it remains unaffected. The method of finding \\(dy\\over dx\\) is explained in the following examples.<\/p>\n

Example 1<\/span><\/strong> : If y = \\(x^{x^{x^{…\\infty}}}\\), find \\(dy\\over dx\\).<\/p>\n

Solution<\/span><\/strong> : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as<\/p>\n

y = \\(x^y\\)<\/p>\n

Taking log on both sides,<\/p>\n

\\(\\implies\\) log y = y logx<\/p>\n

Differentiating both sides with respect to x,<\/p>\n

\\(1\\over y\\)\\(dy\\over dx\\) = \\(dy\\over dx\\) log x + y \\(d\\over dx\\) (log x)<\/p>\n

\\(1\\over y\\)\\(dy\\over dx\\) = \\(dy\\over dx\\) log x + \\(y\\over x\\)<\/p>\n

\\(dy\\over dx\\){\\({{1\\over y} – log x}\\)} = \\(y\\over x\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\)\\((1 – y log x)\\over y\\) = \\(y\\over x\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = \\(y^2\\over {x(1 – ylog x)}\\)<\/p>\n

Example 2<\/span><\/strong> : If y = \\(\\sqrt{sinx + \\sqrt{sinx + \\sqrt{sinx + ……. to \\infty}}}\\), find \\(dy\\over dx\\).<\/p>\n

Solution<\/span><\/strong> : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as<\/p>\n

y = \\(\\sqrt{sin x + y}\\)<\/p>\n

Squaring on both sides,<\/p>\n

\\(\\implies\\)  \\(y^2\\)  = sin x + y<\/p>\n

Differentiating both sides with respect to x,<\/p>\n

2y \\(dy\\over dx\\) =cosx +  \\(dy\\over dx\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\)\\((2y – 1)\\) = cos x<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = \\(cos x\\over {2y – 1}\\)<\/p>\n\n\n

\n
Next – Differentiation of Parametric Functions<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Logarithmic Differentiation \u2013 Examples & Formula<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is differentiation of infinite series class 12 with examples. Let’s begin – Differentiation of Infinite Series Sometimes the value of y is given as an infinite series and we are asked to find \\(dy\\over dx\\). In such cases we use the fact that if a term is deleted from a …<\/p>\n

Differentiation of Infinite Series Class 12<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[36],"tags":[317,275,316,318],"yoast_head":"\nDifferentiation of Infinite Series Class 12 - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is differentiation of infinite series class 12 with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiation of Infinite Series Class 12 - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is differentiation of infinite series class 12 with examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-08T15:11:13+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-22T15:29:39+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Differentiation of Infinite Series Class 12\",\"datePublished\":\"2021-09-08T15:11:13+00:00\",\"dateModified\":\"2021-11-22T15:29:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\"},\"wordCount\":293,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"derivative of infinite series\",\"differentiation\",\"differentiation of infinite series\",\"differentiation of infinite series examples\"],\"articleSection\":[\"Differentiation\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\",\"url\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\",\"name\":\"Differentiation of Infinite Series Class 12 - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-09-08T15:11:13+00:00\",\"dateModified\":\"2021-11-22T15:29:39+00:00\",\"description\":\"In this post you will learn what is differentiation of infinite series class 12 with examples.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Differentiation of Infinite Series Class 12\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Differentiation of Infinite Series Class 12 - Mathemerize","description":"In this post you will learn what is differentiation of infinite series class 12 with examples.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/","og_locale":"en_US","og_type":"article","og_title":"Differentiation of Infinite Series Class 12 - Mathemerize","og_description":"In this post you will learn what is differentiation of infinite series class 12 with examples.","og_url":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/","og_site_name":"Mathemerize","article_published_time":"2021-09-08T15:11:13+00:00","article_modified_time":"2021-11-22T15:29:39+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Differentiation of Infinite Series Class 12","datePublished":"2021-09-08T15:11:13+00:00","dateModified":"2021-11-22T15:29:39+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/"},"wordCount":293,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["derivative of infinite series","differentiation","differentiation of infinite series","differentiation of infinite series examples"],"articleSection":["Differentiation"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/","url":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/","name":"Differentiation of Infinite Series Class 12 - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-09-08T15:11:13+00:00","dateModified":"2021-11-22T15:29:39+00:00","description":"In this post you will learn what is differentiation of infinite series class 12 with examples.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/differentiation-of-infinite-series\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/differentiation-of-infinite-series\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Differentiation of Infinite Series Class 12"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/5135"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=5135"}],"version-history":[{"count":8,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/5135\/revisions"}],"predecessor-version":[{"id":5215,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/5135\/revisions\/5215"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=5135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=5135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=5135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}