{"id":7958,"date":"2021-11-11T17:12:15","date_gmt":"2021-11-11T11:42:15","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7958"},"modified":"2021-11-11T18:06:49","modified_gmt":"2021-11-11T12:36:49","slug":"what-is-the-differentiation-of-esinx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-differentiation-of-esinx\/","title":{"rendered":"What is the differentiation of \\(e^{sinx}\\) ?"},"content":{"rendered":"

Solution :<\/h2>\n

Let y = \\(e^{sinx}\\). Putting u = sinx , we get<\/p>\n

y = \\(e^u\\) and u = sinx<\/p>\n

\\(\\therefore\\)\u00a0 \\(dy\\over du\\) = \\(e^u\\) and \\(du\\over dx\\) = cosx<\/p>\n

Now, \\(dy\\over dx\\) = \\(dy\\over du\\) \\(\\times\\) \\(du\\over dx\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = \\(e^u\\)cosx = \\(e^{sinx}\\)cosx<\/p>\n

Hence, the differentiation of \\(e^{sinx}\\) with respect to x is \\(e^{sinx}\\)cosx.<\/p>\n

\n

Questions for Practice<\/h3>\n

What is the differentiation of cosx sinx ?<\/a><\/p>\n

What is the differentiation of sin square x or \\(sin^2x\\) ?<\/a><\/p>\n

What is the differentiation of 1\/sinx ?<\/a><\/p>\n

What is the differentiation of \\(sin x^2\\) ?<\/a><\/p>\n

What is the differentiation of log sin x ?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let y = \\(e^{sinx}\\). Putting u = sinx , we get y = \\(e^u\\) and u = sinx \\(\\therefore\\)\u00a0 \\(dy\\over du\\) = \\(e^u\\) and \\(du\\over dx\\) = cosx Now, \\(dy\\over dx\\) = \\(dy\\over du\\) \\(\\times\\) \\(du\\over dx\\) \\(\\implies\\) \\(dy\\over dx\\) = \\(e^u\\)cosx = \\(e^{sinx}\\)cosx Hence, the differentiation of \\(e^{sinx}\\) with respect to x …<\/p>\n

What is the differentiation of \\(e^{sinx}\\) ?<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[65,43],"tags":[],"yoast_head":"\nWhat is the differentiation of \\(e^{sinx}\\) ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the differentiation of (e^{sinx}) with respect to x by using chain rule.\" \/>\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\/what-is-the-differentiation-of-esinx\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the differentiation of \\(e^{sinx}\\) ? 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