What is the result of applying the divergence operator to the vector function A = x^2y i - xyz j + yz^2 k?

The result of applying the divergence operator to the vector function A = x²y i - xyz j + yz² k is div A = 2xy - xz + 2yz.

To find the divergence of the vector function A, we compute the partial derivatives of its components. The divergence operator V·A gives the result by taking the partial derivative of the coefficient of i with respect to x, the coefficient of j with respect to y, and the coefficient of k with respect to z. Thus, we have: div A = ∂(x²y)/∂x + ∂(-xyz)/∂y + ∂(yz²)/∂z = 2xy - xz + 2yz.