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Math Help - partial second derivative multiple variables

  1. #1
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    partial second derivative multiple variables

    I can't find the solution to this problem:
    is says z=f(x,y) with x= 2s +3t and y=3s-2t. i have to find zss and zst.
    Do i have to use chain rule or something else?
    thanks

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  2. #2
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    Quote Originally Posted by benoitpouliot5757 View Post
    I can't find the solution to this problem:
    is says z=f(x,y) with x= 2s +3t and y=3s-2t. i have to find zss and zst.
    Do i have to use chain rule or something else?
    thanks

    First, this is not a problem in differential equations and really belongs in the "Calculus" section. In any case, yes, you use the chain rule:
    \frac{\partial z}{\partial s}= \frac{\partial z}{\partial x}\frac{\partial x}{\partial s}+ \frac{\partial z}{\partial y}\frac{\partial y}{\partial s}.

    Then, of course, to get the second derivatives, do it again.
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  3. #3
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    i know i to get xs and ys but how do i get the zx and zy. The answer of the problem is : zss=4f11 + 12f12 + 9f22. i don't understand why there are 3 terms.
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