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Math Help - Multivariable Chain Rule Help!

  1. #1
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    Multivariable Chain Rule Help!

    Suppose f is a differentiable function of x and y, and g(r,s) = f(2r-s,s^2-4r). Calculate dg/dr at (1,2) and dg/ds at (1,2) given that f(1,2)=6, g(1,2)=3, df/dx(1,2)=2 and df/dy(1,2)=5.

    Thanks for reading my question!
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  2. #2
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    bump, someone help please?
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  3. #3
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    Quote Originally Posted by MathTooHard View Post
    Suppose f is a differentiable function of x and y, and g(r,s) = f(2r-s,s^2-4r). Calculate dg/dr at (1,2) and dg/ds at (1,2) given that f(1,2)=6, g(1,2)=3, df/dx(1,2)=2 and df/dy(1,2)=5.

    Thanks for reading my question!

    Put x = 2r - s, y = s^2 - 4r ==> g(r,s) = f(x(r,s),y(r,s)) ==>

    dg/dr = (df/dx)(dx/dr) + (df/dy)(dy/dr) = (df/dx)*2 + (df/dy)*(-4), and since at (1,2) we have (df/dx)(1,2) = 2 and (df/dy)(1,2) = 5, we get....well, now you end the argument.

    Tonio
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  4. #4
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    Thanks.

    What about dg/ds? That s^2 term is giving me bid headaches.
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  5. #5
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    Quote Originally Posted by MathTooHard View Post
    Thanks.

    What about dg/ds? That s^2 term is giving me bid headaches.

    It's EXACTLY similar as dg/dr but with s!

    Tonio
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  6. #6
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    I get -2+10s for dg/ds. From here, do I plug in 2 for s?
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