Unformatted text preview: + y 2 − φ ( x,y ) 2 = 1 and φ (1 , − 1) = 2; the theorem tells us that φ ( x,y ) is di±erentiable at x = 1, y = − 1, with ∂φ ∂x (1 , − 1) = − ∂f/∂x ∂f/∂z = − 8 − 4 = 2 and ∂φ ∂y (1 , − 1) = − ∂f/∂y ∂f/∂z = − − 2 − 4 = 1 2 ....
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 Fall '08
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 Calculus, implicit function theorem

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