The Total Differential

If f is a function of several variables, the total differential enables us to find the change in f as the function moves a small distance between two pointsand We find all the partial derivativesthen the total derivative(1) and this is roughly equal to

with the degree of accuracy increasing asand get closer together.

We evaluate (1) at

Example: Iffindand estimate the change inasmoves along a curve betweenand