Derivative of one functional by another functional

Question

I have two functionals, $F(h, \nabla h)$ and $G(h, \nabla h)$. I'd like to calculate

$\frac{\delta F}{\delta G}$

Since functional derivatives also follow the chain rule, would I be correct in thinking:

$\frac{\delta F}{\delta G} = \frac{\delta F}{\delta h} \cdot \left(\frac{\delta G}{\delta h}\right)^{-1}$

like this link?

Thanks