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Math Help - Multivariable/generalized chain rule -- Need help!

  1. #1
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    Multivariable/generalized chain rule -- Need help!

    I know how to apply the generalized chain rule for functions of this type:
    z=u^2+v^2, u=x^2y and v=xy
    ∂z/∂u=∂z/∂u * ∂u/∂x+∂z/∂v * ∂v/∂x etc.

    I came across a function of this type:
    z=f(u,v), u=x^2y^2 and v=5x+1
    Because of the f(u,v), I don't know how to proceed! Anyone could give me a hint on how to find partial derivatives of this function? What is it that I don't understand?

    Thanks!
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  2. #2
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    Re: Multivariable/generalized chain rule -- Need help!

    Hey tweakedsam.

    What kind of derivative are you trying to find? Can you give an example?
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  3. #3
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    Re: Multivariable/generalized chain rule -- Need help!

    I don't understand how the second situation is different from the first. In both cases z depends on u and v, u depends on x and y, and v depends on x and y.

    Is it because you have to leave \frac{\partial{z}}{\partial{u}} as just \frac{\partial{f}}{\partial{u}}? You can't calculate it any further without knowing more about f, right?

    - Hollywood
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