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Math Help - Use the Chain Rule to find the indicated partial derivatives

  1. #1
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    Use the Chain Rule to find the indicated partial derivatives

    25. u = x^2 + yz, x = pr cos(theta), y = pr sin(theta), z = p + r;

    Du/Dp, Du/Dr, Du/D(theta) when p = 2, r = 3, theta = 0


    Du/Dp etc. are the partial derivatives.


    Thanks.
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  2. #2
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    I believe:

     \frac {du}{dp} = 2(x)(\frac {dx}{dp}) + (y)(\frac {dz}{dp}) + (\frac {dy}{dp})(z)

    The same process is true for the other partial derivatives.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sixstringartist View Post
    I believe:

     \frac {du}{dp} = 2(x)(\frac {dx}{dp}) + (y)(\frac {dz}{dp}) + (\frac {dy}{dp})(z)

    The same process is true for the other partial derivatives.
    you are correct.

    by the chain rule: \frac {du}{dp} = \frac {du}{dx} \cdot \frac {dx}{dp} + \frac {du}{dy} \cdot \frac {dy}{dp} + \frac {du}{dz} \cdot \frac {dz}{dp}

    for \frac {du}{dr} replace p with r in the formula above

    for \frac {du}{d \theta} replace p with \theta in the formula above
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