Question

Find the directional derivative of the function f(x, y) = 3eˣ sin(y) at the point (0, π/3) in the direction of the vector v = (-6, 8).

Answer 1

To find the directional derivative of the function f(x, y) = 3eˣ sin(y) at the point (0, π/3) in the direction of the vector v = (-6, 8), calculate the gradient vector (∇f) and evaluate the dot product of (∇f) and v.

Step-by-step explanation:

To find the directional derivative of the function f(x, y) = 3eˣ sin(y) at the point (0, π/3) in the direction of the vector v = (-6, 8), we can use the formula:

Dvf = (∇f) · v

First, we need to calculate the gradient vector (∇f) which consists of the partial derivatives of f with respect to x and y:

∇f = (∂f/∂x, ∂f/∂y)

Then, evaluate (∇f) · v, substituting the values of (∇f), and v. This will give us the directional derivative.