Let $\quad\displaystyle \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y}+\frac{\partial f}{\partial z} = g(x,y,z)\;$.
Is there a better notation for writing the above?
Given $g$, can $f$ always be found?
Given $g$, is there a unique $f$ that satisfies the above equation?
Is there a name given to this equation?