Discussion Forum

 If g is the inverse of  a function f and   $f'(x)=\frac{1}{1+x^{5}}$  , then g'(x) is equal to

Answer:

Explanation:

Here 'g' is the inverse of f(x)

    $\Rightarrow$    fog(x)= x

On differentiating w.r.t x , we get

 $f'\left\{g(x)\right\}\times g'(x)=1$

$g'(x)=\frac{1}{f'(g(x))}=\frac{1}{\frac{1}{1+\left\{g(x)\right\}^{5}}}$

                                       $[ \because f'(x)=\frac{1}{1+x^{5}}]$

                   $g'(x)=1+\left\{g(x)\right\}^{5}$