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## 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.

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