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Math Help - Differential Check

  1. #1
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    Differential Check

    Where did i go wrong on the second part? I keep getting the same answer and this thing doesnt show me the answer.

    Differential Check-screen-shot-2013-10-10-2.16.31-am.png
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  2. #2
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    Re: Differential Check

    Are these partial derivatives?
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  3. #3
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    Re: Differential Check

    Hello, tastylick!


    \text{Given: }\:w \:=\:\frac{9x+y}{3z-2y}

    \text{Then: }\:\frac{\partial w}{\partial y} \:=\:\frac{1\cdot(3z-2y) - (\text{-}2)(9x+y)}{(3z-2y)^2}

    . . . . . . . . =\:\frac{3z - 2y + 18x + 2y}{(3z-2y)^2}

    . . . . . . . . =\:\frac{3z+18x}{(3z-2y)^2}
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  4. #4
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    Re: Differential Check

    The "total differential" of f(x, y, z) is \frac{\partial f}{\partial x}dx+ \frac{\partial f}{\partial y}dy+ \frac{\partial f}{\partial z}dz
    so your problem appears to be with the partial derivative of \frac{9x+ y}{3z- 2y}.

    By the "quotient rule" that is \frac{(1)(3z- 2y)- (-2)(9x+ y)}{(3z- 2y)^2}= \frac{3z+ 18x}{(3z- 2y)^2}
    You have left out the "x"!
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