Can quotient of two differentiable function be non differentiable?

Question

If I have two differentiable functions, can their quotient be not differentiable?

Answer 1

In general, we will have $(\frac fg)'=\frac{f'g-fg'}{g^2}$ from the quotient rule, so the only way this can fail is when $g=0$ (but then the quotient itself is not defined)