If differentiable function f(x) is inverse of g(x) then is equal to

JEE MainMathematicsModerateDifferentiation

If differentiable function f(x) is inverse of g(x) then
$f^{'}'(g(x))$ is equal to

Show answer and solution

f(g(x)) = x \Rightarrow f^{'}(g(x)) \cdot g^{'}(x) = 1

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

\Rightarrow f^{''}(g(x)) \cdot g^{'}(x) = \frac{- 1}{{(g^{'}(x))}^{2}}g^{''}(x)

\Rightarrow f^{''}(g(x)) = \frac{- g^{''}(x)}{{(g^{'}(x))}^{3}}

Source: Grass-G / M-12 Mathematics Paper 2 Nov.docx

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