Directional derivative and angles.
Consider a surface S given by the equation z = f(x,y) where f(x,y)= xe^(4x^2-y^2).
(a) Find the directional derivative Duf in the direction of u parallel to v = 3i+4j at the point A=(1,2).
(b) Find the angles THETAx and THETAy of the directional vector u in (x,y) plane relative to x and y axes, respectively, at which the maxim of Duf at the point A is reached.
For (a) I used the formula Duf(x,y) = Fx(x,y)cosTHETA + Fy(x,y)sinTHETA. I took the first order partial derivatives and plugged in the point A=(1,2). For THETA (and this is where I might have made a mistake) I used 3/4 because the directional derivative is parallel to v = 3i+4j.