If g is inverse of f and f'(x)=1/(1+x^n) then g'(x) equals

Since g is the inverse of f.

∴  fog(x) = x for all x

$\Rightarrow \frac{d}{d x}\{fog(x)\}=1 $ for all x

$\Rightarrow f'(g(x)) . g'(x)=1$

$\Rightarrow f'\{g(x)\}=\frac{1}{g(x)}$

$\Rightarrow \frac{1}{1+[g(x)]^n}=\frac{1}{g'(x)}$                   $\left[∵ f'(x)=\frac{1}{1+x^n}\right]$

$\Rightarrow g'(x)=1+[g(x)]^n$