Answer Happy

Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable.

Prove that

(a) ∂x/∂y *
∂y/∂x = 1

(b) ∂y/∂z *
∂z/∂x*
∂x/∂y = −1

(c) ∂z/∂y = −
(∂F/∂y) / (∂F/∂z)