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Thread: Differentials

  1. #1
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    Differentials

    Hi,
    How do you do this question? I don't understand the wording.
    Differentials-kj.png
    Do i simply find du and dv seperately, WRT to x and y?
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  2. #2
    MHF Contributor

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    Re: Differentials

    You could find the derivatives of u and v separately, but that would require solving for u and v as functions of x and y. Can you do that?

    I would use "implicit differentiation". For example, differentiating the first equation, u^2v- u= x^3- 2y^3, with respect to x, wq have 2uv du/dx+ u^2 dv/dx- du/dx= 3x^2. As "differentials in terms of the differentials of x and y" that would be 2uv du+ u^2 dv= 3x^2 dx. Differentiating with respect to y would give 2uv du/dy- du/dy= 6y^2 or, as "differentials", 2uv dv- du= 6y^2 dy.
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