gradient and plane equations

You case has 3 and 2 variables:
F(x,y)=f(p(x,y),q(x,y),r(x,y))F(x,y) = f(p(x,y), q(x,y), r(x,y))and the chain rule for FxF_x is:
Fx=Fppx+Fqqx+Frrx\frac{\partial F}{\partial x} = \frac{\partial F}{\partial p} \cdot \frac{\partial p}{\partial x} + \frac{\partial F}{\partial q} \cdot \frac{\partial q}{\partial x} + \frac{\partial F}{\partial r} \cdot \frac{\partial r}{\partial x}Can you work out or find the formula for FyF_y?

Your case is somewhat simpler: pp and qq are trivial, and rr is called gg.
 
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