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Math Help - Need help with a partial derivative of a multivariate function

  1. #1
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    Need help with a partial derivative of a multivariate function

    Hi, I have to work out the first partial derivative of the following function:

    f(x,y)=(x^3+y)sin(1/(x^2+y^2))

    So, what I am getting is:

    f'(x, y)=(3x^2)sin(1/(x^2+y^2))-((x^3+y)2y) / (x^2+y^2)^2 * cos(1/(x^2 + y^2))

    But the answer is supposed to be almost identical, except that it is -((x^3+y)2x) instead of -((x^3+y)2y). I have done it several times with the chain rule and I keep on getting the same thing... I would really appreciate it if someone could show me how to get the second half :/. Thanks a lot in advance!!!
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  2. #2
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    Re: Need help with a partial derivative of a multivariate function

    Quote Originally Posted by juanma101285 View Post
    Hi, I have to work out the first partial derivative of the following function:

    f(x,y)=(x^3+y)sin(1/(x^2+y^2))

    So, what I am getting is:

    f'(x, y)=(3x^2)sin(1/(x^2+y^2))-((x^3+y)2y) / (x^2+y^2)^2 * cos(1/(x^2 + y^2))

    But the answer is supposed to be almost identical, except that it is -((x^3+y)2x) instead of -((x^3+y)2y). I have done it several times with the chain rule and I keep on getting the same thing... I would really appreciate it if someone could show me how to get the second half :/. Thanks a lot in advance!!!
    Are you evaluating \displaystyle \begin{align*} \frac{\partial f}{\partial x} \end{align*} or \displaystyle \begin{align*} \frac{\partial f}{\partial y} \end{align*}?
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  3. #3
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    Re: Need help with a partial derivative of a multivariate function

    Sorry, I understand it now.... I mixed up the formulae and was somehow trying to evaluate both :/
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