# Directional derivative question

1. Mar 31, 2014

### julz127

1. The problem statement, all variables and given/known data
rate of change of $f(x,y) = \frac{x}{(1+y)}$ in the direction (i-j) at the point (0,0)

2. Relevant equations

3. The attempt at a solution
$∇f(x,y) = \frac{1}{(y+1)}\hat{i} - \frac{x}{(y+1)^2}\hat{j}$

$D_u = ( f_x, f_y) \bullet ( 1, -1 )$

$D_u = \frac{(y+x+1)}{(y+1)^2}$

Wolfram and the answer sheet is telling me that there should be a $\sqrt{2}$ in the denominator, but I can't figure out where it comes from, thanks.

Last edited: Mar 31, 2014
2. Mar 31, 2014

### Dick

The vector you want to dot the grad with should be a unit vector pointed in the direction i-j. That's what 'in the direction' means.