# Thread: stuck at the middle of the differential part

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

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

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

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

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

3. $\displaystyle \frac{dG}{dx} = \frac{\partial G}{\partial x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial z}{\partial x}$
$\displaystyle 0 = \frac{\partial G}{\partial x}\cdot 0+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial z}{\partial x}$
$\displaystyle \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=\frac{\partial y}{\partial x}$
Similarly
$\displaystyle \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}}=\frac{\partial z}{\partial y}$
$\displaystyle \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=\frac{\partial x}{\partial z}$
$\displaystyle \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}\cdot \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}} \cdot \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=-1$
See that each term at the numerator eliminates with one at the denominator.

4. Originally Posted by vincisonfire
$\displaystyle \frac{dG}{dx} = \frac{\partial G}{\partial x}\frac{\partial x}{\partial x}+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial z}{\partial x}$
$\displaystyle 0 = \frac{\partial G}{\partial x}\cdot 0+\frac{\partial G}{\partial y}\frac{\partial y}{\partial x} +\frac{\partial G}{\partial z}\frac{\partial Z}{\partial x}$
$\displaystyle \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}=\frac{\partial y}{\partial x}$
Similarly
$\displaystyle \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}}=\frac{\partial z}{\partial y}$
$\displaystyle \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=\frac{\partial x}{\partial z}$
$\displaystyle \frac{- \frac{\partial G}{\partial x}}{\frac{\partial G}{\partial y}}\cdot \frac{- \frac{\partial G}{\partial y}}{\frac{\partial G}{\partial z}} \cdot \frac{- \frac{\partial G}{\partial z}}{\frac{\partial G}{\partial x}}=-1$
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