Question

Find the directional derivative of f(x,y,z)=xy+z^2 at (10, 9, 8) in the direction of i\hat+j\hat+k\hat

Answer 1

I'm told that the directional derivative is grad(f) dotted with the unit vector. I did that and found \[x+y+2z\]is the directional derivative. I am not sure where to go from here. I tried substituting (10,9,8) into this, but that is not the right answer.

Answer 2

you need to dot grad(f) with the unit vector *of v=(10,9,8)* which is
u=v/|v|
that is, scalar divide the direction vector by its magnitude, then dot it with grad(f)

Answer 3

Oh, thank you! I assumed since I was given unit vectors i j and k, I was to dot with those.

Answer 4

you're welcome