course Mth 275 Section 12.5:This section took some thinking about to fully understand, but I? comfortable with all the material now. I did have a problem with a couple of the questions. #51 gives z = xy + f(x^2-y^2) and says to show that y(δz/δx) ?x(δz/δy) = y^2 ?x. Using w = x^2 ?y^2, I can get to x(δz/δy) + y(δz/δx) = 0, but no further. #60 gives F(x,y,z) = 0 and G(x,y,z) = 0 with y=y(x) and z = z(x), and asks for dy/dx and dz/dx in terms of the partial derivatives of F and G. I came up with dy/dx = (δF/δx)/( δF/δy) = (δG/δx)/( δG/δy) and dz/dx = (δF/δx)/( δF/δz) = (δG/δx)/( δG/δz), but this seems too simple.