{"id":8511,"date":"2021-11-22T21:35:03","date_gmt":"2021-11-22T16:05:03","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8511"},"modified":"2021-11-22T21:40:15","modified_gmt":"2021-11-22T16:10:15","slug":"differentiate-xsinx-with-respect-to-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/differentiate-xsinx-with-respect-to-x\/","title":{"rendered":"Differentiate \\(x^{sinx}\\) with respect to x."},"content":{"rendered":"

Solution :<\/h2>\n

Let y = \\(x^{sinx}\\). Then,<\/p>\n

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

log y = sin x.log x<\/p>\n

\\(\\implies\\) y = \\(e^{sin x.log x}\\)<\/p>\n

By using logarithmic differentiation<\/a>,<\/p>\n

On differentiating both sides with respect to x, we get<\/p>\n

\\(dy\\over dx\\) = \\(e^{sin x.log x}\\)\\(d\\over dx\\)(sin x.log x)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = \\(x^{sin x}{log x {d\\over dx}(sin x) + sin x {d\\over dx}(log x)}\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = \\(x^{sin x}(cos x.log x + {sin x\\over x}\\))<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let y = \\(x^{sinx}\\). Then, Taking log both sides, log y = sin x.log x \\(\\implies\\) y = \\(e^{sin x.log x}\\) By using logarithmic differentiation, On differentiating both sides with respect to x, we get \\(dy\\over dx\\) = \\(e^{sin x.log x}\\)\\(d\\over dx\\)(sin x.log x) \\(\\implies\\) \\(dy\\over dx\\) = \\(x^{sin x}{log x {d\\over dx}(sin …<\/p>\n

Differentiate \\(x^{sinx}\\) with respect to x.<\/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":"\nDifferentiate \\(x^{sinx}\\) with respect to x. - Mathemerize<\/title>\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\/differentiate-xsinx-with-respect-to-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiate \\(x^{sinx}\\) with respect to x. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let y = (x^{sinx}). Then, Taking log both sides, log y = sin x.log x (implies) y = (e^{sin x.log x}) By using logarithmic differentiation, On differentiating both sides with respect to x, we get (dyover dx) = (e^{sin x.log x})(dover dx)(sin x.log x) (implies) (dyover dx) = (x^{sin x}{log x {dover dx}(sin … Differentiate (x^{sinx}) with respect to x. 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