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Math Help - chain rule (jacobian matrix)

  1. #1
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    chain rule (jacobian matrix)

    z = sin (u) cos (v); u=3x^2, v=x-3y

    \left(\begin{array}{cc}cos(u)cos(v)&-sin(v)sin(u)\end{array}\right) \left( \begin{array}{cc} 6x&0\\1&-3\end{array}\right) =\left(\begin{array}{cc}6xcos(3x^2)cos(x-3y)-sin(x-3y)sin(3x^2)\\0-3sin(x-3y)sin(3x^2)\end{array}\right)

    I have a feeling this is incorrect
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  2. #2
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    Re: chain rule (jacobian matrix)

    It is incorrect, but very close. You want the transpose of the final matrix (it should be two columns instead of two rows).
    Thanks from Jonroberts74
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  3. #3
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    Re: chain rule (jacobian matrix)

    \left( \begin{array}{cc}6xcos(3x^2)(x-3y) - sin(x-3y)sin(3x^2)&3sin(x-3y)sin(3x^2)\end{array}\right)

    thanks, got the matrix multiplication mixed up
    Last edited by Jonroberts74; June 28th 2014 at 10:54 AM.
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