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Math Help - Partial Derivatives Question?

  1. #1
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    Post Partial Derivatives Question?

    so, i've been having trouble with this particular problem regarding proofs and partial derivatives. i get how to evaluate them but i just can't understand this problem.

    ok,so for this problem, u = f(x,y), where x = e^s cost and y = e^s sin t.
    show that

    (∂u/∂x)^2+(∂u/∂y)^2 = e^-2s[(∂u/∂s)^2+(∂u/∂t)^2]

    please help
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  2. #2
    MHF Contributor

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    Re: Partial Derivatives Question?

    The only thing you can write for \frac{\partial u}{\partial x} is \frac{\partial f}{\partial x}= f_x and similarly for \frac{\partial u}{\partial y}. For \frac{\partial u}{\partial s}, use the chain rule: \frac{\partial u}{\partial s}= \frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+ \frac{\partial u}{\partial y}\frac{\partial y}{\partial s}.
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