Let $F(u,v)$ be a function of two variables. Let $F_u(u,v) = G(u,v)$, and $F_v(u,v) = H(u,v)$. Find $f'(x)$ for each of the following cases (your answers should be written in terms of $G$ and $H$).

(a) $f(x)=F(x,3)$: then
$f'(x) =$

(b) $f(x)=F(2,x)$: then
$f'(x) =$

(c) $f(x)=F(x,x)$: then
$f'(x) =$

(d) $f(x)=F(3 x,x^{5})$: then
$f'(x) =$