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

$\begin{array}{1 1}(A)\;1+x^5\\ (B)\;5x^4 \\(C)\;\large\frac{1}{1+\{g(x)\}^5} \\(D)\;1+\{g(x)\}^5 \end{array} $

1 Answer

Given : $f^{-1} (x) = g$
$\implies f o g = x$
$\therefore f'(x) = f'(g(x))$
Given $\begin{align*}f'(x)= \frac{1}{1+x^5} \end{align*}$
$\begin{align*}\implies f'(x) = \frac{1}{1 + [g(x)]^5} \end{align*}$
answered Apr 7, 2014 by meena.p
edited Nov 7 by priyanka.c
 

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