stuck at the middle of the differential part

**vincisonfire** · November 8th 2008, 04:50 PM

$\frac{dG}{dx} = \frac{\partial G}{\partial x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial Z}\frac{\partial Z}{\partial x}$

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

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

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

**vincisonfire** · November 8th 2008, 05:08 PM

$ \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 0+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial z}{\partial x} $
$ \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=\frac{\partial y}{\partial x} $
Similarly
$ \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}}=\frac{\partial z}{\partial y} $
$ \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=\frac{\partial x}{\partial z} $
$ \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 $
See that each term at the numerator eliminates with one at the denominator.

**yzc717** · November 8th 2008, 05:47 PM

Originally Posted by vincisonfire

$ \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 0+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial Z}{\partial x} $
$ \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=\frac{\partial y}{\partial x} $
Similarly
$ \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}}=\frac{\partial z}{\partial y} $
$ \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=\frac{\partial x}{\partial z} $
$ \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 $
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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