Question

Find the derivative of
f (x, y) = xy/ (x+ y)
at the point (2, -1) in the direction of 6i + 8j

i got < fx, fy> = < y^2/(x+y)^2 , x^2/(x+y)^2> , and plug in that bad boy (2,-1)

then im lost , we get <1,4> x <6,8>

Answer 1

\[fx = \frac{y^2}{ (x+ y)^2}\]those look good

Answer 2

if the surface is not defined as a vector function but a scalar function that might throw us for a loop

Answer 3

my calculus is 1200 pages, im scared to open it

Answer 4

calculus book *

Answer 5

i get the idea, they want the slope at the direction 6i + ...

Answer 6

like this?

Answer 7

\[cos(t)=\frac{u.v}{|u||v|}\]

Answer 8

if thats helps

Answer 9

hmmmm , i will come back and work on it, thanks
maybe paul has a solution one sec

Answer 10

good luck with it :)

Answer 11

hey i found a nifty graphing calculator
www.romanlabs.com

Answer 12

http://mathinsight.org/directional_derivative_gradient_examples

Answer 13

so you get the derivative to be <1,4> and dot that to a unit vector to get:

1u + 4u

the directional vector is the unitified and subbed into this:

<6,8>/10 = <3/5,4/5>

1(3/5) + 4(4/5)

3/5 + 16/5 = 19/5