## The concept of differential

**Definition:** the Differential of the function at point is defined as a product of the derivative at this point, that is, the increase of the argument (denoted by or — read "teh y")

For any point : if you have , then

## Table of differentials of elementary functions:

**An example of finding a differential in mathematics: **

**The differential is composed of functions**

## The main property of differential

Differential of a function-the main linear (i.e. proportional ) part of the increment function

## The finding of the differential. The geometrical meaning of the differential.

**The rules for finding the differential remains the same as that for finding the derivative, you only need to multiply the derivative on DX.**

If in formula (when there are and ), then for small . Let us denote Then for small

For example:

a) , that is **(for small )** ;

b) , that is **(for small )**

**An example of calculating the differentials ** For numerical calculations we take

Then the formula gives

that is