15. Mathematical formula list

Basic mathematical formulas are shown below.

Item Explanation

combination

The number of combinations to obtain r elements out of n elements is given by following formula.

For example, there are three (ab, bc, ca) types on how to take 2 items from 3 items data a, b, c.

Permutation

The number of permutations to obtain r elements out of n elements is given by following formula.

For example, there are six ab, ba, bc, cb,ca, ac) types of permutation to take 2 elements from 3 elements data a, b, c.

Exponent

The number in which a is nth times multiplied is expressed by , and is called nth exponent. Following formulas are basic calculation of exponent.

Trigonometric table

Trigonometric table is defined as follows by using the right-angled triangle.

The mutual relationship of the trigonometric table is expressed by the following formula.

root

That is, at the time of , it is said that a is c root of b, and expressed by . The following relation is established in the root.

Among the root, is called as imaginary number, and expressed by i.

logarithm

When , is called logarithm of c that considers b as base.

Also, the following relation is established when the base is same.

Among the logarithm, the logarithm that considers 10 as base is called common logarithm. or expressed as
Moreover, the logarithm that considers e=2.718281828 … as base is called the natural logarithm. Or expressed by

derivation

The derivation formula of a typical function is shown as follows.

integration

The integration formula of a typical function is shown as follows.