Question

Find the gradient field of the function g(x,y,z)=9xy.

Answer 1

To find the gradient field of the function g(x,y,z)=9xy, calculate the partial derivatives with respect to each variable: ∂g/∂x = 9y, ∂g/∂y = 9x, and ∂g/∂z = 0. The gradient field is (∂g/∂x, ∂g/∂y, ∂g/∂z) = (9y, 9x, 0).

Step-by-step explanation:

To find the gradient field of the function g(x,y,z)=9xy, we need to calculate the partial derivatives with respect to each variable. The gradient of a function is given by ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z). In this case, ∂g/∂x = 9y, ∂g/∂y = 9x, and ∂g/∂z = 0. Therefore, the gradient field of g(x,y,z)=9xy is (∂g/∂x, ∂g/∂y, ∂g/∂z) = (9y, 9x, 0).