Finding directional deriviative

[shemer77]

Homework Statement

Find the directional derivative of f at P in the direction of a
f(x,y)=(x*e^y)-(y*e^x); P(0,0);a=5i-2j

my answer came out to 0

The Attempt at a Solution

i got the unit vector from p to a, which came out to <5/√(29),-2/√(29))
and also the partial derivatives
i then took the gradient of f and got <0,0>
and then the directional derivative which came out to 0, is this right?

 

[HallsofIvy]

"Directional vector from p to a" is meaningless. a is not a point- it is already the vector giving the direction. Just divide it by its length to get a unit vector.

The gradient vector, at (0, 0), is NOT 0. Do it again. What do you get for the gradient before you set x= 0, y= 0?