I'm trying to prove that: $\frac{\partial g(f(\vec{a}))}{\partial\vec{v}} = g'(f(\vec{a}))\cdot\frac{\partial f(\vec{a})}{\partial \vec{v}}$
I have tried the following: $\frac{\partial g(f(\vec{a}))}{\partial\vec{v}} = \lim_{h \to 0}\frac{g(f(\vec{a}+h\vec{v}))-g(f(\vec{a}))}{h}$
But I don't know if this step is correct or how to continue. Any tips are welcome!