how do I find this vector?

Question

I have to find the directional derivative of f(x,y) = x^2 + 4y^2 at P = (3,2) in the direction pointing to the origin.

do I have to find a vector u, in the direction pointing to the origin? how do I find this vector?

Answer 1

P = (3,2) is a vector pointing from the origin to the point P. The vector pointing in the opposite direction will be -P.
To find the directional derivative you need a unit vector pointing in this direction. Divide the vector -P by the magnitude of P to get a unit vector.
Finally, to get the actual answer
Take the dot product of the gradient of f evaluated at P with the unit vector that you found.