Expressing one gradient in terms of the other

Suppose I have the following relation:
$mathbf{v}=t|mathbf{k}|^{t-2}mathbf{k}$ where $mathbf{v}$ and $mathbf{k}$ are $d-$dimensional vectors and $tinmathbb{R}$.

I want to express $nabla_{mathbf{v}}$ in terms of $nabla_{mathbf{k}}$. Is it possible? What is the expression?

I think it should just be $nabla_{mathbf{v}} = frac{1}{t|mathbf{k}|^{t-2}}nabla_{mathbf{k}}$ but that is possibly not correct.