JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1
Let $f$ and $g$ be differentiable functions on $\mathbf{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbf{R}$, $g'(a)=5$ and $g(a)=b$, then $f'(b)$ is equal to :
Differentiation and its Application
Solution
Concept. Differentiate $f(g(x))=x$ at $x=a$. Formulas used. (1) $f'(g(x))\,g'(x)=1$Step 1 - At $x=a$. By (1), $f'(b)\cdot5=1$, so $f'(b)=\frac15$. Answer: (A)