Directional derivative

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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!
 

Answers and Replies

  • #2
Dick
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What happened to the 5 in the denominator of 3/5?
 
  • #3
hover
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What happened to the 5 in the denominator of 3/5?

Hmm... that's a good question :P

D_uf(6,6) = -2/5+3/10
 

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