The derivative of f(x)=x^(tan^-1 x) with...

The derivative of `f(x)=x^(tan^-1 x)` with respect to `g(x)=sec^-1(1/(2x^2-1))` is

A

`1/2sqrt(1-x)x^(tan^-1x)[(logx)/(1+x^2)+(tan^-1x)/x]`

B

`-1/2sqrt(1-x^2)x^(tan^-1x)[log(tan^-1x)+x(1+x^2)tan^-1x]`

C

`(-2tan^-1x[(logx)/(1+x^2)+(tan^-1x)/x])/sqrt(1-x^2)`

D

`-1/2sqrt(1-x^2)x^(tan^-1x)[(log_x)/(1+x^2)+(tan^-1x)/x]`

Verified by Experts

The correct Answer is:

D

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