Finding the divergence

Question

Find the divergence of F^-> (x, y, z) = < xcos⁻¹y, z/ (y² + 1) , 3xz² + 2y > at (2, 0, −1).

Answer 1

To find divergence use del• F(x,y,z) where del is the operator ∂/∂x i + ∂/∂y j + ∂/∂z k. Taking the dot product gives ∂F/∂x=cos^-1y ∂F/∂y =-2yz/(y²+1)² ∂F/∂z= 6xz. Now at (2,0,-1) the divergence is π/2 +0 -12 =π/2 -12.