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Math Help - Partial Derivative of x^y

  1. #1
    Member mybrohshi5's Avatar
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    Unhappy Partial Derivative of x^y

    For  f(x,y) = x^2cos(y) - \frac{x^3}{y^2} + x^y

    Find.....  f_x, f_y, f_x_x, f_y_y, f_x_y, f_y_x

    I know how to do this expect i am running into trouble with the x^y term.

    so the x partial derivative ( f_x) of x^y is .... x^yln(x) ????

    and the y partial derivative ( f_y) of x^y is ....  x ????

    Thank you
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  2. #2
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    When you are finding f_x, you treat y as a constant.

    So \frac{\partial}{\partial x}(x^y) = x^{y-1}y.


    When you are finding f_y, you treat x as a constant.

    So \frac{\partial}{\partial y}(x^y) = x^y\ln{x}.
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  3. #3
    Member mybrohshi5's Avatar
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    Perfect that is exactly what i needed

    Thank you so much!
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