Don't know how to do this. Please help!!
Find gradient vector of f(x,y).
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.
$\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