Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = 2ye−x, (0, 6), θ = 2π/3

Answer-

The directional derivative of f(x,y) at (0,6) in the direction θ = 2π/3 is, 7.73

Solution-

The unit vector in the direction of the given angle is

Given that,

Gradient of f(x,y)

Gradient of f(x,y) at (0,6)

= <(-2)(6)(1) , (2)(1)> = <-12 , 2>

The directional derivative of f(x,y) at (0,6) is

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d