Calculate the directional derivative of the given function f

Calculate the directional derivative of the given function f at the point a in the direction parallel to the vector u

f(x, y) = (e^y) cos(x),
a = (π/6, 0)
u = (i − 2j) /√5

I know im supposed to find the gradient and do a dot product with the unit vector but i keep getting the answer wrong. Help would be nice!

Grad(f) = [-(e^y) sin(x)] i + [(e^y) cos(x)] j

At the point a, Grad[f(a)] = [ -1 * 1/2 ] i + [ 1 * √3/2 ] j = (-1/2) i + (√3/2) j

We verify that u is a unit vector (it is).

And the directional derivative is :
Grad[f(a)] . u = -1/2 * 1/√5 + √3/2 * (-2/√5) = -1/(2√5) - √3/√5
= - ( 1/2 + √3 )/√5

Hope this helps