Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

Differentiate x^sinx+(sinx)^cosx with respect to x. - Mathematics

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Differentiate xsinx+(sinx)cosx with respect to x.

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Differentiating both sides with respect to x, we get

`dy/dx=e^(sinx logx)xx d/dx(sinxlogx)+e^(cosxlog sinx)xxd/dx(cosx log sinx)`

`dy/dx=x^(sinx)(sinxxx1/x+logx xx cosx)+(sin)^(cosx)(cosx xx 1/sinx xx cosx +log sinx)`

`dy/dx=x^(sinx)((sinx)/x+cosx logx)+(sinx)^(cosx)((cos^2x)/(sinx)-sinx log sinx)`


Concept: Derivative - Exponential and Log
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2015-2016 (March) All India Set 2 C

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