Question

Find the directional derivative of f(x,y)= sqrt(xy) at P(2,8) in the direction of Q(5,4)

Answer 1

im gonna have to play with this just cause im outta practice :)

Answer 2

ahahahhok, i love you amistre btw :) you save my life constantly

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcIII/DirectionalDeriv.aspx

im reading up on it from this site :)

Answer 4

yah i use that frequently

Answer 5

so, vector from P to Q = Q-P

5,4
2,8
----
<3,-4> since this is a 345 triangle I know the mag = 5 so the unit vector is:

<3/5, -4/5> for that part

Answer 6

I spose del F is next

Answer 7

ok thats where i had trouble because i was not given a specific vector direction. So i need to make one from P to Q?

Answer 8

\[\nabla f(x,y)= sqrt(xy)\]
\[Fx = \frac{y}{2\sqrt{xy}}\]
\[Fy= \frac{x}{2\sqrt{xy}}\]

Answer 9

yes, from P in the direction of Q

Answer 10

ok i think i can do the rest that was my main question. thanks again pal. I am just studying for a midterm i have in 3 hrs :)

Answer 11

Do we then dot these together?

<Fx,Fy> . <3/5,-4/5> ?

Answer 12

midterms are fun lol

Answer 13

they suck my left nut lol. ill be posting a few more questions soon if you could answer id appreciatge it!

Answer 14

if im able :) ill try