Differentials, an aspect of calculus, are important for working with errors of measurement and the propagation of error.
Dr. Donald Simanek discusses their use in Error Calculations Using Calculus. Dr. Mike Coombes discusses their use in Error Propagation Using Calculus Solutions. And Dr. Rhett Allain uses them in the interesting Error Propagation And the Distance To the Sun.
I have not read the articles/essays closely, so I don’t know if there are any mistakes in them. But they illustrate the general idea.
