Find the derivative of `(1+cosx)^(x)` with respect to x. – InterviewSolution

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1.	Find the derivative of `(1+cosx)^(x)` with respect to x.
Answer» Let y=`(1+cosx)^(x)` log y=`log(1+cosx)^(x)` `=xlog(1+cosx)` Differentiate both sides with respect to x. `(1/y)(dy)/(dx)=xcdotd/(dx)log(1+cosx)+log(1+cosx)cdotd/(dx)x` `rArr(dy)/(dx)=y[x/(1+cosx)cdotd/(dx)(1+cosx)+log(1+cosx)]` `rArr(dy)/(dx)=(1+cosx)^(x)[(-xsinx)/(1+cosx)+log(1+cosx)]` Ans.

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