Question

Find the gradient vector field of f. f(x,y,z)=xcos( z
3y
​
) ∇f(x,y,z)=

Answer 1

Explanation:

The gradient vector field (∇f) is found by taking the partial derivatives of f with respect to each variable x, y, and z.

∂f/∂x = cos(z)

∂f/∂y = 3

∂f/∂z = -xsin(z)

Therefore, the gradient vector field ∇f(x,y,z) = (cos(z), 3, -xsin(z))