Question

Multicalculus problem.
let f(x,y)=(x-y)/(x+y), find the directions u and the values of Duf(-1/2,3/2) for which
a) Duf(-1/2,3/2) =is largest
b) Duf(-1/2,3/2) = 0
c) Duf(-1/2,3/2)=1

Answer 1

duf?

Answer 2

directional derivative

Answer 3

any ideas

Answer 4

Df=(2y/((x+y)^2,-2x/(x+y)^2)
(2y/((x+y)^2,-2x/(x+y)^2).(-1/2,3/2)

Answer 5

D=nabla

Answer 6

(2y/((x+y)^2,-2x/(x+y)^2).(-1/2sqrt2,3/2sqrt2)

Answer 7

I think I see what your saying. Thank you

Answer 8

sorry
(2y/((x+y)^2,-2x/(x+y)^2).(-1/sqrt10,3/2sqrt10)

Answer 9

(2y/((x+y)^2,-2x/(x+y)^2).(-1/sqrt10,3/sqrt10)

Answer 10

(:

Answer 11

-2/sqrt10(1/(x+y)) I guess this is the answer..

Answer 12

I just looked at this web site

http://tutorial.math.lamar.edu/Classes/CalcIII/DirectionalDeriv.aspx#PD_DirectDeriv_Ex2a