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Math Help - Differential question

  1. #1
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    Differential question

    I have to find differential (it can be full-differential, but I am not sure if it is the right word in english) as described on the attachment.
    I actually don't understand what I have to calculate.
    I am used to use the last formula on the attachment to calculate differentials. I am not sure if this formula is suitable for the first equation on the attachment.
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  2. #2
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    Quote Originally Posted by totalnewbie View Post
    I have to find differential (it can be full-differential, but I am not sure if it is the right word in english) as described on the attachment.
    I actually don't understand what I have to calculate.
    I am used to use the last formula on the attachment to calculate differentials. I am not sure if this formula is suitable for the first equation on the attachment.
    Remember implicit differentiation?

    xyz = e^z

    Take the partial "differential" of both sides with respect to x, that is take y to be a constant for a moment:
    yz(dx) + xy(dz) = e^z(dz)

    Then
    yz + xy(dz/dx) = e^z(dz/dx) <-- These are now partial derivatives.

    dz/dx = yz/(e^z - xy) = yz/(xyz - xy)

    Similarly:
    xz(dy) + xy(dz) = e^z(dz)

    xz + xy(dz/dy) = e^z(dz/dy)

    dz/dy = xz/(e^z - xy) = xz/(xyz - xy)

    Thus:
    dz = [yz/(xyz - xy)]dx + [xz/(xyz - xy)]dy <-- The "d's" are now full differentials. Sorry about the notational confusion!

    -Dan
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