differentiate the following function with respect to x

x^(tan^-1(x))

let y=x^tan^-1x

taking log on both sides, we get

logy=tan^-1xlogx

Now diif. w.r.to x by using product rule,we get

(1/y). dy/dx=tan^-1x.(1/x)+logx.[1/(1+x²)]

dy/dx= x^tan^-1x[tan^-1x.(1/x)+logx.{1/(1+x²)}]

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty