Why isn't my directional derivative coming out right?

[hover]

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) = \nablaf*u : dot product

The Attempt at a Solution

\nablaf = <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!

 

[Dick]

What happened to the 5 in the denominator of 3/5?

 

[hover]

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