If $\| \, \, \|$ denotes the euclidean norm on $\mathbb{R}^n$, is $f: x \mapsto \dfrac{x}{\| x \|^2}$ differentiable on $\mathbb{R}^n \backslash \{ 0 \}$ ?
I tried to use the fact that $\| \, \, \|$ is differentiable on $\mathbb{R}^n \backslash \{ 0 \}$, or to compute $f(x + h) - f(x)$, but couldn't get anything from there.
Thank you for your help.