Even function/Differentiable/Relation/Exercise

Let ${}f\colon \mathbb {R} \rightarrow \mathbb {R}$ be an even function, and suppose that it is differentiable in the point ${}x$. Show that ${}f$ is also differentiable in the point ${}-x$ and that the relation

${}f'(-x)=-f'(x)\,$

holds.

Create a solution