Example 1

The most important particular case is that where E is one of the fields $\mathbf{R}$ or $\mathbf{C}$: if $f$ is a function with real or complex values, differentiable at the point $x_0$, and such that $f(x_0) \neq 0$, then $1/f$ has derivative equal to $-f'(x_0)/(f(x_0))^2$ at $x_0$.