Differentiable functions

From the Theory of Limits (Chapter 3) it is clear that if the derivative of a function exists for a certain value of the independent variable, the function itself must be continuous for that value of the variable.

The converse, however, is not always true, functions having been discovered that are continuous and yet possess no derivative. But such functions do not occur often in applied mathematics, and in this book only differentiable functions are considered, that is, functions that possess a derivative for all values of the independent variable save at most for isolated values.