Math Help - Directional derivative problem

1. Directional derivative problem

I am suppose to find the directional derivative for the function f(x,y,z) = xy + z^2

at the point (2,3,4) in the direction of a vector making an angle of 3pi/4 with the grad f(2,3,4)

I have done several with this function with other specific directions but this one is confusing me.

I know the grad is y i + x J + 2z k so at (2,3,4) this would be 3i + 2j + 8 k but where do I go from here???? Please someone nudge or push me in the correct direction!!!! Thanks

2. Originally Posted by Frostking
I am suppose to find the directional derivative for the function f(x,y,z) = xy + z^2

at the point (2,3,4) in the direction of a vector making an angle of 3pi/4 with the grad f(2,3,4)

I have done several with this function with other specific directions but this one is confusing me.

I know the grad is y i + x J + 2z k so at (2,3,4) this would be 3i + 2j + 8 k but where do I go from here???? Please someone nudge or push me in the correct direction!!!! Thanks
The directional derivative of f in the direction of a unit vector v is the scalar product grad(f).v. In this case, you don't know v, but you do know the formula u.v = |u||v|cos(θ) for the scalar product of two vectors, where θ is the angle between them.

3. Directional derviative question

I remember that the dot product of two vectors is equal to their magnitude's multiplied by the cos of the angle between them but since I do not have v or mag of v how does this allow me to solve this question???? I am still lost.

4. Originally Posted by Frostking
I remember that the dot product of two vectors is equal to their magnitude's multiplied by the cos of the angle between them but since I do not have v or mag of v how does this allow me to solve this question???? I am still lost.
Well v is a unit vector so its magnitude is 1, and the angle between v and grad(f) is given as 3π/4 so you can work out its cosine. Problem solved!