Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 21

The derivative of a function is one of its fundamental properties. It represents the rate of change of the slope of the function: in other words, how fast the function changes with respect to changes in the independent variable. We focus on real-valued functions of a real variable.

Let . Then the derivative of f at x (if it exists) is defined by the limit for :

(1.7)

This limit may not exist at certain points, and it is possible to define right-hand and left-hand limits, that is, one-sided derivatives.

Some results that we learn in high school are:

(1.8)

A composite function is a function that we can differentiate using the chain rule that we state as follows:

(1.9)

A simple example of use is:

More challenging examples of composite functions are: