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Math Help - stuck at the middle of the differential part

  1. #1
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    stuck at the middle of the differential part

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  2. #2
    Senior Member vincisonfire's Avatar
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     \frac{dG}{dx} = \frac{\partial G}{\partial  x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial  y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial  Z}\frac{\partial Z}{\partial x}

     0 = \frac{\partial G}{\partial  x}\cdot 1+\frac{\partial G}{\partial  y}\cdot 0 +\frac{\partial G}{\partial  Z}\frac{\partial Z}{\partial x}

     - \frac{\partial G}{\partial  x}=\frac{\partial G}{\partial  Z}\frac{\partial Z}{\partial x}

     \frac{- \frac{\partial G}{\partial  x}}{\frac{\partial G}{\partial  Z}}=\frac{\partial Z}{\partial x}
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  3. #3
    Senior Member vincisonfire's Avatar
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    <br />
\frac{dG}{dx} = \frac{\partial G}{\partial  x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial  y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial  z}\frac{\partial z}{\partial x}<br />
    <br />
0 = \frac{\partial G}{\partial  x}\cdot 0+\frac{\partial G}{\partial  y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial  z}\frac{\partial z}{\partial x}<br />
    <br />
\frac{- \frac{\partial G}{\partial  x}}{\frac{\partial G}{\partial  y}}=\frac{\partial y}{\partial x}<br />
    Similarly
    <br />
\frac{- \frac{\partial G}{\partial  y}}{\frac{\partial G}{\partial  z}}=\frac{\partial z}{\partial y}<br />
    <br />
\frac{- \frac{\partial G}{\partial  z}}{\frac{\partial G}{\partial  x}}=\frac{\partial x}{\partial z}<br />
    <br />
\frac{- \frac{\partial G}{\partial  x}}{\frac{\partial G}{\partial  y}}\cdot \frac{- \frac{\partial G}{\partial  y}}{\frac{\partial G}{\partial  z}} \cdot \frac{- \frac{\partial G}{\partial  z}}{\frac{\partial G}{\partial  x}}=-1<br />
    See that each term at the numerator eliminates with one at the denominator.
    Last edited by vincisonfire; November 8th 2008 at 09:16 PM.
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  4. #4
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    Quote Originally Posted by vincisonfire View Post
    <br />
\frac{dG}{dx} = \frac{\partial G}{\partial x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial z}{\partial x}<br />
    <br />
0 = \frac{\partial G}{\partial x}\cdot 0+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial Z}{\partial x}<br />
    <br />
\frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=\frac{\partial y}{\partial x}<br />
    Similarly
    <br />
\frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}}=\frac{\partial z}{\partial y}<br />
    <br />
\frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=\frac{\partial x}{\partial z}<br />
    <br />
\frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}\cdot \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}} \cdot \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=-1<br />
    See that each term at the numerator eliminates with one at the denominator.


    Thanks so much, I am still working on it myself, see what i got wrong through the solutuion you gave me.

    I just having a hard time on differential equation with multi-variables
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