Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b\inR, g'(a)=5 and g(a) = b, then f'(b) is equal to :

Engineering

Mathematics

Derivative of Inverse Function

Question

Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b $\in$ R, g'(a)=5 and g(a) = b, then f'(b) is equal to :

$\frac{2}{5}$

$\frac{1}{5}$

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f(g(x)) = x

⇒ f'(g(x)). g'(x) = 1

Put x = a

⇒ f'(g(a)) g'(a) = 1

⇒ f'(b) × 5 = 1

$\Rightarrow f' (b) = \frac{1}{5}$