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Math Help - Partial derivatives.

  1. #1
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    Partial derivatives.

    Hi
    I am trying to study partial derivatives but my maths books does not cover it very well-the examples are much too difficult.
    I am looking at a previous exam question -can some body tell me if i am on the right track?

    Find partial derivatives (df/dx) and (df/dy) -sorry have not worked out how to put proper symbols in yet.

    f(x,y)=e^(xy). Cos(y)

    i will get the partial derivative when x varies and y is constant first.

    Let u=e^(xy) and v=cos(y)

    f(x,y)= u. v

    Use the product rule.

    for the product rule i need du/dx when y is treated as a constant

    du/dx=e^(xy).y

    I also need dv/dx when x is treated as a constant

    dv/dx=0

    therefore: the product rule gives df/dx=cos (y^2). e^xy

    The is the partial derivative df/dx -i.e when x varies and y is a constant.

    Can somebody tell me if this is correct? I will leave the df/dy part until i know my method is correct.

    Can recommend a good site that gives easy worked examples that i can follow. Both my maths books do not explain this very well
    regards
    John
    Last edited by mr fantastic; August 30th 2011 at 08:28 PM.
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  2. #2
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    Re: Partial derivatives-help!

    Quote Originally Posted by celtic1234 View Post
    Hi
    Find partial derivatives (df/dx) and (df/dy) -sorry have not worked out how to put proper symbols in yet.
    f(x,y)=e^(xy). Cos(y)
    Why not just do it?
    f(x,y)=e^{xy}\cos(y)

    f_x (x,y) = ye^{xy} \cos (y)
    and
    f_y (x,y) = xe^{xy} \cos (y)-e^{xy}sin(y)
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  3. #3
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    Re: Partial derivatives-help!

    you make it look very easy-which it is-maybe i need to look at it simpler
    thanks
    John
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