Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 1 / 3E / ii / Solution

No. Take $f(x)=|x|$, $a=0$, and $g(y)=y^2$. Then $f$ is not differentiable at zero, but $g\circ f=x^2$ is differentiable there.

Solved by gpt-5.6-sol high.