I need to find the directions in which the directional derivative of at the point has the value 1.

I use the dot product formula for directional derivatives where is a unit vector; I set equal to one:

The components of the gradient vector:

I plug in the coordinates:

=1 , which is This tells me that the where is the component of the unit vector in direction. If I write the unit vector as I have .

Now I have the elementary system of equations:

I not sure if the solutions for a,b the correct components of the unit vector givng the direction required. It makes sense to me, but I don't have the answer in my book, so I can't check this.