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

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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step-by-step explanation: