# Free Online Applications

List of available free online applications:

## Math

### Intermediate Level

1. online differentiation
This application enables finding derivatives for complex functions that depend on more than one variable. Let us consider a simple case. For instance, our function has the following form: f(x, y, z) = x^2 + y^2 + z^2. As the first step, an user should choose which variable among all three (x, y and z) is its differentiation variable i. e. over which variable the f function will be differentiated. Let us assumed that it is x variable. The rest of variables (y and z) are treated as parameters and kept constant during differentiation. After successful calculations, the program should display an obtained result in two forms. The first of them is longer and allows to conclude a way in which the final result is obtained. On the other hand, the second formula is shorter and simplified (if a simplification is available). When the final result is known one can plot the function under consideration (i. e. f function), its analytic and numerical derivative. The latter one, is obtained numerically from the base function f. To make these plots one need to set numerical values of our parameters: y and z and, of course, set the numerical range in which the variable x varies. Finally, one can compare both analytic and numerical derivative to find out if the obtained solution is correct or not.