Let $f:\mathbb{R}^d \setminus \left \{ 0 \right \} \to \mathbb{R}$ be a differentiable function.
Prove that $f$ is homogenous of order $\kappa$ ($\forall t>0, p\in D: f(tp)=t^{\kappa}f(p)$) if and only if $\forall p \in D$, $\left \langle \nabla f(p), p \right \rangle = \kappa f(p)$
Not sure what to do, ideas are welcome.