How do you find the derivative of #y = x^(cos x)#?

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Answer 1 · 2016-01-17T10:26:39

#y' =x^cos x(cos x/x-sin x ln x)#

Take the logarithm of both sides #y=x^(cos x)#

#ln y=cos x(ln x)#

differentiate both sides of the equation

#1/y*y'=cos x*1/x*1+ln x*(-sin x)#

#y'= y*(cos x/x-sin x* ln x)#

replace #y# by its equivalent

#y'=x^cos x(cos x/x-sin x ln x)#