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## Homework Statement

Find the directional derivative of f(x, y) = (xy)

^{1/2}at P(6, 6) in the direction of Q(2, 9)

## Homework Equations

D_uf(x,y) = [tex]\nabla[/tex]f*u : dot product

## The Attempt at a Solution

[tex]\nabla[/tex]f = <y

^{1/2}/(2x

^{1/2}),x

^{1/2}/(2y

^{1/2})>

vector PQ = Q-P = <2-6,9-6> = <-4,3>

unit vector u of PQ is

u = PQ/|PQ| = <-4,3>/(4^2+3^2)

^{1/2}= <-4/5 , 3/5>

D_uf(x,y) = <y

^{1/2}/(2x

^{1/2}),x

^{1/2}/(2y

^{1/2})> * <-4/5 , 3/5> = -2y

^{1/2}/(5x

^{1/2}) + 3x

^{1/2}/(2y

^{1/2})>

so

**D_uf(6,6) = -2/5+3/2**

Somehow this isn't the right answer so where did I go wrong?

Thanks!