Differentials

Multi-variable functions have differentials just like single-variable functions do.

Given the function $z=f(x,y)$ the differential $dz$ or $df$ is given by:

$$dz=f_{x}dx+f_{y}dy\text{ or }df=f_{x}dx+f_{y}dy$$

Given the function $w=g(x,y,z)$, the differential is given by:

$$dw=g_{x}dx+g_{y}dy+g_{z}dz$$