Differential of a function, finding the differential

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

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