When you calculate a directional derivative, you need to do the inner product with a unit vector. The unit vector in the direction $\displaystyle \vec{i}+2\vec{j}$ is $\displaystyle \frac{1}{\sqrt{5}}\vec{i}+\frac{2}{\sqrt{5}}\vec{j }$. So when you take the dot product, you should get $\displaystyle \frac{4}{\sqrt{5}}$. I assume your answer 5/sqrt(5) is a typo.
- Hollywood
It's not? I calculated $\displaystyle \nabla(x^2y) = \vec{i}\frac{\partial}{\partial{x}}(x^2y) + \vec{j}\frac{\partial}{\partial{y}}(x^2y) = 2xy\vec{i}+x^2\vec{j}$, and substituting $\displaystyle x=y=-1$ gives $\displaystyle 2\vec{i}+\vec{j}$.
What am I missing?
- Hollywood