Total Differential

It's quite simple, if I give you an expression:

$$z = x y$$

You will get: $$\begin{align*} dz &= (xy)^\prime_x dx + (xy)^\prime_y dy \\ \\ dz &= \frac{\partial z}{\partial x} dx + \frac{\partial z}{\partial y} dy \\ \\ dz &= y \cdot dx + x \cdot dy \end{align*}$$