Gradient / rate of change problem

Question

Example: Let $f(x,y)=x^2+\cos{y}$. The rate of change at $f$ at $(1,0)$ in the direction of $<1,1>$ is:

A. $1$ B. $\sqrt{2}$ C. $\frac{\sqrt{3}}{2}$ D. $\pi$ E. $0$

I'm confused on how to start this. Am I supposed to find the gradient, plug in $(1,0)$ and take the dot product of this with $<1,1>$?

Thanks!

Answer 1

You are looking for a directional derivative, which is indeed as you say, except you have to dot with the unit vector in the direction of $(1,1)$, and $(1,1)$ has length $\sqrt2$.

Answer 2

The answer is b What u thought of doing is correct. But after finding the gradient take the dot product of the gradient with the unit vector along the direction of <1,1>