If w = w(x, y, z) is given implicitly by F(x, y, z, w) = 0, find a formula
for both ∂w/∂z and ∂^2w/∂y∂z . You may assume that each function is sufficiently
differentiable and anything you divide by during the process of your
solution is non-zero.
The Attempt at a Solution
I know in class, my professor showed us how to implicitly differentiate using this method where if y = y(x) and F(x,y) = 0, you can do dF/dx = ∂F/∂x + ∂F/∂y*dy/dx = 0 and dy/dx = -(∂F/∂x)/(∂F/∂y),
Is this the kind of formula my professor wants us to find?