Find a unit vector and the rate of change Could anyone help me answer this question? Or point me in the right direction?
Find a unit vector in the direction in which f increases most rapidly at P and find the rate of change of f at p in that direction.
$$f(x,y) = \sqrt{\frac{xy}{x+y}}; \qquad P(1,1)$$
http://i.imgur.com/ecr8HIA.png 

A vector in the direction of most change is $(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})$. Divide by its length to find a unit vector.
Add the unit vector to P and evaluate f to find the rate of change.
