If g is inverse of f and $f'(x)=\frac{1}{1+x^n}$ then g'(x) equals

$1+x^n$ $1+[f(x)]^n$ $1+[g(x)]^n$ none of these

$1+[g(x)]^n$

Since g is the inverse of f. ∴  fog(x) = x for all x $\Rightarrow \frac{d}{d x}\{fog(x)\}=1 $ for all x $\Rightarrow f'(g(x)) . g'(x)=1$ $\Rightarrow f'\{g(x)\}=\frac{1}{g(x)}$ $\Rightarrow \frac{1}{1+[g(x)]^n}=\frac{1}{g'(x)}$                   $\left[∵ f'(x)=\frac{1}{1+x^n}\right]$ $\Rightarrow g'(x)=1+[g(x)]^n$