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

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: