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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 = <y1/2/(2x1/2),x1/2/(2y1/2)>
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) = <y1/2/(2x1/2),x1/2/(2y1/2)> * <-4/5 , 3/5> = -2y1/2/(5x1/2) + 3x1/2/(2y1/2)>
so D_uf(6,6) = -2/5+3/2
Somehow this isn't the right answer so where did I go wrong?
Thanks!