I am not sure how to proceed with this question:
Construct counterexamples for the following statements.
(a) If a function $g(x)$ is differentiable at $x=a$ and a function $f(x)$ is not differentiable at $g(a)$, then the function $(f\circ g)(x)$ is not differentiable at $x=a$.
(b)If a function $g(x)$ is not differentiable at $x=a$ and a function $f(x)$ is differentiable at $g(a)$, then the function $(f\circ g)(x)$ is not differentiable at $x=a$.
(c) If a function $g(x)$ is not differentiable at $x=a$ and a function $f(x)$ is not differentiable at $g(a)$, then the function $(f\circ g)(x)$ is not differentiable at $x=a$.
For (a) I have begun by outlining what I know:
g'(a) exists
f'(g(a)) does not exist
(f\circ g)'(x)=f\;'(g(x))\cdot g'(x)
Which leaves me stuck because then (f\circ g)'(a)=f\;'(g(a))\cdot g'(a) and it is stated that $f(x)$ is not differentiable at $g(a)$.