Let φ : $\mathbb{R}^n → \mathbb{R}$ be a $C^1$ function such that $∀t ∈ \mathbb{R}$ we have $φ(tx) = t^{42}φ(x)$. Prove that $∀x ∈ R^n$, $x·∇φ(x) = 42φ(x)$.
If someone could help me out with this problem that'd be great.
Let φ : $\mathbb{R}^n → \mathbb{R}$ be a $C^1$ function such that $∀t ∈ \mathbb{R}$ we have $φ(tx) = t^{42}φ(x)$. Prove that $∀x ∈ R^n$, $x·∇φ(x) = 42φ(x)$.
If someone could help me out with this problem that'd be great.
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