Question

Find the derivative of the function at P₀ in the direction of A.

f(x, y, z) = x*y + y*z + z*x
P₀ = (-2, 2, -3)
A = 3i + 2j - 6k

Answer 1

To find the derivative of the function in the given direction at a specific point, we can use the directional derivative formula. First, calculate the gradient of the function. Then, evaluate the gradient at the given point and compute the dot product with the direction vector. Finally, divide the result by the magnitude of the direction vector.

Step-by-step explanation:

To find the derivative of the function at point P₀ in the direction of A, we can use the directional derivative formula:

∇f(P₀) • A / ||A||

First, calculate the gradient of f(P₀) by taking the partial derivatives of f(x, y, z). Then, evaluate the gradient at P₀ to get the directional derivative in the direction of A. Finally, divide the directional derivative by the magnitude of A to obtain the derivative in the direction of A at P₀.