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Math Help - Total Differential

  1. #1
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    Total Differential

    Find the total differential:

    u=arcsen \sqrt\frac{xz}{y}
    du=?

    My teacher give to us this formule: \Delta f (x,y) \approx \frac{\delta f}{\delta x} |p\Delta x + \frac{\delta f}{\delta y}|p\Delta y + \frac{\delta f}{\delta z}|p\Delta z

    but in this exercice he just dont give the point "P" and the valous of \Delta n
    i use this formule: \Delta f (x,y) \approx \frac{\delta f}{\delta x}  + \frac{\delta f}{\delta y} + \frac{\delta f}{\delta z}
    and the result was:
    part 1: http://i.imgur.com/W46hP.jpg
    part 2: http://i.imgur.com/uYTek.jpg
    is this correct??
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Total Differential

    Hi again Chipset3600!

    The proper formula is:

    df(x,z,y) = {\partial f \over \partial x}dx + {\partial f \over \partial y}dy + {\partial f \over \partial z}dz

    I have some trouble understanding your scans, but they do not look right.

    Let's define g(x,y,z)=\sqrt{xz \over y}.
    And let's define u(v)=\arcsin v.

    What is {\partial g \over \partial x}?

    And {du \over dv}?
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  3. #3
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    Re: Total Differential

    dg/dx is the first derivative of G as a function of x

    and du/dv is the total diferencial of function u, rite??
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Total Differential

    Quote Originally Posted by Chipset3600 View Post
    dg/dx is the first derivative of G as a function of x
    Yes.
    It's called the partial derivative of g as a function of x.


    Quote Originally Posted by Chipset3600 View Post
    and du/dv is the total diferencial of function u, rite??
    It's just the derivative of u with respect to v.
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  5. #5
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    Re: Total Differential

    well did a mistake in the formule, buts this means that my result isn's correct ?
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: Total Differential

    Well, I couldn't make sense of your first scan, so just now I skipped to the second one.

    And yes!
    Your partial derivatives are correct (except for \partial u \over \partial y that should have a minus sign).

    However, for the total derivative du you shouldn't have added them as you did.
    Each of them should be multiplied by dx, dy, and dz respectively.
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  7. #7
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    Re: Total Differential

    One more time thank you very match!
    We most talk!
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