1.12.2 Vector analysis

Problem: Find the gradient of the scalar field \( U(x, y, z)= \) \( \arctan \left(\frac{z}{y+z}\right) \) at an arbitrary point and at the point \( M_{0}=(1,1,0) \). For the resulting vector field \( \bar{a}= \) \( \nabla U(x, y, z) \) find \( \operatorname{div} \bar{a} \) and \( \operatorname{rot} \bar{a} \) at the point \( M_{0} \).