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## Homework Statement

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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 $$7/2\sqrt{5}$$.