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

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answerhappygod
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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

Post by answerhappygod »

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)
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