Define $F$ as $$F(x,y,u,v) = x^3e^{uv} + vy^2\sin{\left(y^3\right)}$$ where $u(x,y) = x^2y$ and $v(x,y) = xy^3$.
Define $f(x,y) = F(x,y,u(x,y),v(x,y)$.
Determine $\dfrac{\partial F}{\partial x}$ and $\dfrac{\partial f}{\partial x}$.
How to do this for $F$ and $f$ respectively? Aren't $F$ and $f$ the same? I'm confused. Thanks