Mathematics Cheat Sheet: Derivatives, Vectors, Probability, and More

Derivative Table

f (x) = K f ‘(x) = 0
f (x) = x f ‘(x) = 1
f (x) = kx f ‘(x) = k
f (x) = kx + b f ‘(x) = k
f (x) = xⁿ f ‘(x) = nx^n-1
f (x) = u (x) + v (x) f ‘(x) = u’ (x) + v ‘(x)
f (x) = u (x) * v (x) f ‘(x) = u (x) * v’ (x) + v (x) * v ‘(x)
f (x) = u (x) / v (x) f ‘(x) = [v (x) * u’ (x) – u (x) * v ‘(x)] / [v (x)]²
f (x) = [u (x)]ⁿ f ‘(x) = n[u (x)]^n-1 * u’ (x)
f (x) = sin x f ‘(x) = cos x
f (x) = sin [u (x)] f ‘(x) = cos u * u’
f (x) = cos x f ‘(x) = – sin x
f (x) = cos u f ‘(x) = – sin u * u’
f (x) = tan x f ‘(x) = sec² x
f (x) = tan u f ‘(x) = sec² u * u’
f (x) = cot x f ‘(x) = -csc² x
f (x) = cot u f ‘(x) = -csc² u * u’
f (x) = sec x f ‘(x) = sec x * tan x
f (x) = sec u f ‘(x) = tan u sec u * u’
f (x) = csc x f ‘(x) = – csc x * cot x
… (Continued)

Descriptive and Inferential Statistics

Descriptive statistics: Classification and description of a dataset.

Inferential statistics: Interpreting the results obtained with the descriptive techniques for making decisions.

Statistician: Global descriptive feature of a total sample of research.

Frequency polygon: Graphic lines usually plotted on a frequency histogram.

In mathematics, especially in linear algebra, a matrix of dimensions n × n is said to be invertible, nonsingular, or regular if there is a matrix B of dimensions n × n such that AB = BA = I_n,

where I_n denotes the identity matrix of order n (dimension n × n) and the product used is the usual matrix product. A matrix that is not invertible is said to be a singular matrix.

The inverse of the matrix A is unique. This is denoted by A^-1.

Properties of the Inverse Matrix

The inverse of the product of two matrices is the product of changing the reverse order:

Company Departments

Departments:
– Production Department: This is the one who is responsible for developing the product with which the company sells. In the Company of the tertiary sector do not exist.
– Finance Department: Responsible for seeking alternative sources of funding for the company.
– Human Resources Department: Its main function is to select and recruit workers, formalize contracts, process payroll and social insurance, in addition to ensuring compliance with labor laws. They are in charge of relations with the entire team of the company.
– Business Department: The marketing function includes all activities necessary to reach the consumer goods and services produced by the company. Through these functions, 3 subfunctions are performed that are … (Continued)

Bodies and Substance

Bodies and substance: Physics, biological and geological.
Subject: What extends all the way and can boast.
Kinds of matter: Melting point, density, smell, taste, color …
General properties: Mass, volume …
Body:
External properties: Shape, volume, area, length …
Internal properties: They depend on the nature of the substance that is formed.
Materials systems: Well-defined set of material bodies. Each one of these bodies is known as a component of the system.
Open: If matter and energy exchange with the outside.
Closed: If the foreign exchange only energy, no matter.
Isolated: If it is impossible any exchange of matter and energy with the outside.
… (Continued)