Question

Find the directional derivative of f at the given point in the direction indicated by the angle θ.
f(x,y) = sin(x + 2y)
(4, -2)
θ = 3π/4

Answer 1

So first off, what do you know and what can you find out? This is asking multiple things, so just take it one step at a time. The main three parts I'm seeing are:

Find directional derivative, ok that's not so bad.

Then find out what it is at a specific given point, ok we can plug this in.

But then see what amount is in the direction 3pi/4, which is basically going to be looking at a vector and seeing how much of it points in the same direction as a unit vector. This sounds complicated, but isn't, since your unit vector in the direction 3pi/4 is just <cos(3pi/4), sin(3pi/4)>.