Don't know how to do this. Please help!!

Find gradient vector of f(x,y).

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- May 5th 2008, 02:33 AM4sweet2005Find gradient vector
Don't know how to do this. Please help!!

Find gradient vector of f(x,y). - May 5th 2008, 02:42 AMMoo
Hello,

$\displaystyle f(x,y)=\sqrt{\frac{x+y}{x-y}}$

The gradient vector of a function is defined as following :

$\displaystyle \vec{\nabla}f=\left(\frac{\partial f}{\partial x} \ , \ \frac{\partial f}{\partial y} \right)$

For example, $\displaystyle \frac{\partial f}{\partial x}$ is the derivative of f, considering that x is the variable and y is a constant. - May 5th 2008, 02:47 AM4sweet2005
This is what I just worked out ( 2y/(x-y)^2 , -2y/(x-y)^2 ), not sure if that's the answer?

Please help! - May 5th 2008, 02:54 AMtopsquark
$\displaystyle \frac{\partial }{\partial x} \left ( \sqrt{\frac{x+y}{x-y}} \right ) $

$\displaystyle = \frac{1}{2} \cdot \frac{1}{\sqrt{\frac{x+y}{x-y}}} \cdot \left ( \frac{(1)(x - y) - (x + y)(1)}{(x - y)^2} \right ) $

$\displaystyle = \sqrt{\frac{x-y}{x+y}} \cdot \left ( \frac{-2y}{2(x - y)^2} \right ) $

$\displaystyle = -\frac{y}{(x - y)^{3/2} (x + y)^{1/2}}$

Try your y derivative again.

-Dan