In 21 Definition & Properties we define the derivative as a limit of difference quotients, and investigate the basic properties of differentiable functions
In 22 Theorems & Applications we prove the Mean Value Theorem, a cornerstone result in real analysis and give some applications; from understanding maxima and minima to L’Hospitals rule.
In 23 Power Series we investigate the differentiability of power series
In 24 Elementary Functions we use calculus to single out the natural exponential, natural logarithm, and natural units (radians) for the trigonometric functions.