differentiate the following function with respect to x

(1+cos x)^x

y=(1+cosx)^x

^{taking log on both sides}

logy=xlog(1+cosx)

diff.w.r.to x , we get

(1/y)dy/dx=x.(1/(1+cosx))(-sinx)+log(1+cosx).1

dy/dx=(1+cosx)^x[-xsinx/(1+cosx) +log(1+cosx)]

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