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Math Help - Partial Derivative Help

  1. #1
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    Partial Derivative Help

    Okay so I know how to get partial derivatives. One thing that I'm having trouble with is finding f_xy, because I'm not sure if I'm actually doing it correctly.

    For example, lets say:

    z=xy(5-x)(y-2)

    f_x=(5-2x)y(y-2)
    f_y=x(5-x)(2y-2)

    to my understanding.... to get f_xy you have to take the partial derivative of y and then using that function now take it into respect of x.

    So the answer i got was

    f_xy=(5-2x)(2y-2)
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  2. #2
    Member mohammadfawaz's Avatar
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    Hello,

    Your answer is correct. However you explained the method of getting f_{xy} in wrong way (you flipped x and y!).
    In fact, f_{xy} = (f_x)_y. That is, you find f_x then you differentiate what you get with respect to y.

    Hope that helps
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  3. #3
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    pickslides's Avatar
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    Quote Originally Posted by radioheadfan View Post

    to my understanding.... to get f_xy you have to take the partial derivative of y and then using that function now take it into respect of x.
    Well its really the other way around but i think you could find f_{xy} = f_{yx} this time.

    First of all take z=xy(5-x)(y-2) and expand it out to get

    z= 5xy^2-10xy-x^2y^2+2x^2y

    which is really

    f(x,y,z) = 5xy^2-10xy-x^2y^2+2x^2y-z

    Now taking the derivative with respect to x you get

    f_{x} = 5y^2-10y-2xy^2+4xy

    Now take this f_{x} with respect to y

    f_{xy} = 10y-10-4xy+4x

    And you are done.
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