{"id":5137,"date":"2021-09-08T20:42:42","date_gmt":"2021-09-08T15:12:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5137"},"modified":"2021-11-22T20:43:56","modified_gmt":"2021-11-22T15:13:56","slug":"differentiation-of-parametric-functions","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/differentiation-of-parametric-functions\/","title":{"rendered":"Differentiation of Parametric Functions"},"content":{"rendered":"

Here you will learn differentiation of parametric functions with example.<\/p>\n

Let’s begin –<\/p>\n

Differentiation of Parametric Functions<\/h2>\n

Sometimes x and y are given as functions of a single variable e.g. x = \\(\\phi\\)(t), y = \\(\\psi\\)(t) are two functions of a single variable. In such a case x and y are called parametric functions or parametric equations and it is called the parameter. To find \\(dy\\over dx\\) in case of parametric functions, we first obtain the relationship between x and y\u00a0 by eliminating the parameter t and then we differentiate it with respect to x. But, it is not always convenient to eliminate the parameter. Therefore, \\(dy\\over dx\\) can also be obtained by the formula<\/p>\n

\n

\\(dy\\over dx\\) = \\(dy\/dt\\over dx\/dt\\)<\/p>\n<\/blockquote>\n

Example<\/span><\/strong>\u00a0: find \\(dy\\over dx\\) where x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t<\/p>\n

Solution <\/span><\/strong>: We have,<\/p>\n

x = a{cos t + \\({1\\over 2} log tan^2 {t\\over 2}\\)} and y = a sin t<\/p>\n

\\(\\implies\\) x = a{cos t + \\({1\\over 2} \\times 2 log tan{t\\over 2}\\)} and y = a sin t<\/p>\n

\\(\\implies\\) x = a{cos t + {\\(log tan{t\\over 2}\\)} and y = a sin t<\/p>\n

Differentiating with respect to t, we get<\/p>\n

\\(dx\\over dt\\) = a{-sin t + \\({1\\over tan t\/2}(sec^2{t\\over 2})\\times {1\\over 2}\\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(dx\\over dt\\) = a{-sin t + \\(1\\over 2 sin (t\/2) cos (t\/2)\\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\implies\\)\u00a0 \\(dx\\over dt\\) = a{-sin t + \\(1\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\implies\\)\u00a0 \\(dx\\over dt\\) = a{\\(-sin^2t + 1\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(dx\\over dt\\) = a{\\(cos^2t\\over sint \\)} and \\(dy\\over dt\\) = a cost<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0\\(dy\\over dx\\) = \\(dy\/dt\\over dx\/dt\\) = \\(acost\\over {acos^2t\\over sint}\\)\u00a0<\/p>\n

\\(dy\\over dx\\) = tan t<\/p>\n\n\n

\n
Next – Differentiation of Determinant<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Differentiation of Infinite Series Class 12<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn differentiation of parametric functions with example. Let’s begin – Differentiation of Parametric Functions Sometimes x and y are given as functions of a single variable e.g. x = \\(\\phi\\)(t), y = \\(\\psi\\)(t) are two functions of a single variable. In such a case x and y are called parametric functions or …<\/p>\n

Differentiation of Parametric Functions<\/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":[315,275,314,121],"yoast_head":"\nDifferentiation of Parametric Functions - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the differentiation of parametric functions with example.\" \/>\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-parametric-functions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiation of Parametric Functions - 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