- #1
betamu
- 12
- 3
Homework Statement
[/B]
Find the directional derivative of the function at the given point in the direction of the vector v.
$$g(s,t)=s\sqrt t, (2,4), \vec{v}=2\hat{i} - \hat{j}$$
Homework Equations
$$\nabla g(s,t) = <g_s(s,t), g_t(s,t)>\\
\vec{u} = \vec{v}/|\vec{v}|\\
D_u g(s,t) = \nabla g(s, t) \cdot \vec{u}$$
The Attempt at a Solution
I found $$\nabla g(s, t) =<\sqrt{t}, s/(2\sqrt{t})>$$ which gives $$\nabla g(2,4) = <2, 1/2>$$ and the directional vector to be $$<2/\sqrt{5}, -1/\sqrt{5}>$$ Which gives a dot product of $$5/2\sqrt{5}$$ but my book says that it should be $$7/2\sqrt{5}$$.