JEE-Mains 2014 (11/30)

Calculus Level 3

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

1+x^5

5x^4

1+(g(x))^5

\frac{1}{1+(g(x))^5}

1 solution

Satvik Choudhary
Jun 16, 2015

By definition of inverse $f^{-1}(f (x))=x$

Since f (x) & g (x) are inverse functions

g(f (x))=x

Differentiating with respect to x. $g'(f (x)).f'(x)=1$ Putting the value of f'(x) in the above equation we get $g'(f(x))=x^{5}+1$ Putting x= g (x) in the above equation we get $g'(f(g(x)))=(g(x))^{5}+1$

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

JEE-Mains 2014 (11/30)

1 solution

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