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  4. If g is the inverse of a function f and f '(x)=(1/1+x5), then g' (x) is equal to :

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

JEE MainJEE Main 2014Limits and Derivatives

Solution:

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