Directional derivative question

[julz127]

Homework Statement

rate of change of [itex] f(x,y) = \frac{x}{(1+y)} [/itex] in the direction (i-j) at the point (0,0)

Homework Equations

The Attempt at a Solution

[itex] ∇f(x,y) = \frac{1}{(y+1)}\hat{i} - \frac{x}{(y+1)^2}\hat{j} [/itex]

[itex]D_u = ( f_x, f_y) \bullet ( 1, -1 )[/itex]

[itex]D_u = \frac{(y+x+1)}{(y+1)^2} [/itex]

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

 

[Dick]

Homework Statement

rate of change of f(x,y) = x/(1+y) in the direction (i-j) at the point (0,0)

Homework Equations

The Attempt at a Solution

grad(f(x,y)) = 1/(y+1)i - x/(y+1)^2j

Du = ( f_x, f_y ) dot ( 1, -1 )

Du = (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.

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.