Let's say we have got a function $F(G(B)\cdot C)$, i.e function $F$, which is a function of a function $G$ and variable $C$; also function $G$ is a function of variable $B$. Now I want to obtain the expression for $\partial F/ \partial B$ and $\partial F/ \partial C$.
What I get is:
$$\frac{\partial F}{\partial B}=F'(G(B)\cdot C)\cdot C\cdot G'(B)$$
and:
$$\frac{\partial F}{\partial C}=F'(G(B)\cdot C)\cdot G(B)$$
Now the question is whether $F'(G(B)\cdot C)$ in both equations is the same thing or one is $F_B$ and the second $F_C$. I would appreciate your help.