Question

Compute the directional derivatives of the following functions along unit vectors at the indicated points in directions parallel to the given vector:

Answer 1

To compute the directional derivatives of given functions along unit vectors at specified points parallel to the given vector, use the formula Duf(x, y) = ∇f(x, y) • u, where ∇f(x, y) is the gradient vector of f(x, y) and • represents the dot product.

Step-by-step explanation:

The question is asking to compute the directional derivatives of given functions along unit vectors at specified points parallel to the given vector. To compute the directional derivative of a function f(x, y) along a unit vector u, we use the formula:

Duf(x, y) = ∇f(x, y) • u

where ∇f(x, y) is the gradient vector of f(x, y) and • represents the dot product. We can substitute the components of the unit vector and the function gradient into the formula to compute the directional derivative.