Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right) + {x^2} + {y^2}} \right]\widehat k\,\,$$

Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that

The directional derivative of $$f\left( {x,y} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at point $$P\left( {2,1,3} \right)\,\,$$ in the direction of the vector $$\,\,a = \overrightarrow i - 2\overrightarrow k \,\,$$ is