A selection of free mathematics resources (calculators, graphing calculator, exercises, games, quizzes, course reminders) that allow you to draw and manipulate the usual mathematical functions.
Real functions : Reminder
Real functions definition
A Real function from A to B is defined by giving :

A: starting set

B: arrival set

and a correspondence allowing to associate to any element x of A, one element y of B at most.
Odd and even functions.
 A function is even in `RR` if for any `x in RR` f(x)=f(x)
 A function is odd in `RR` if for `x in RR` f(x)=f(x)
The calculator
can be used to determine whether a function is even or odd.
Graphical representation of real functions
A representative curve of a numerical function f is the set of points with coordinates M(x; y), where y represents the image of x by f.
Here, for example, is the
graphical representation of the function f defined by `f(x)=x^23` obtained with the calculator
.
Graphical representation of an even function.
In an orthogonal reference frame, when a function is even, the yaxis is an axis of symmetry of its graphical representation.
Graphical representation of an odd function
In an orthogonal frame of reference, when a function is odd, the origin O is a center of symmetry of the graphical representation.
Increasing and decreasing functions
f is a function and I is an interval contained in its set of definitions.

To say that f is strictly increasing on I means that for all real numbers u and v of the interval I, the inequality u > v implies f(u) > f(v).

To say that f is strictly decreasing on I means that for all real numbers u and v in the interval I, the inequality u > v implies f(u) < f(v).
Calculating the derivative of a function
Usual formulas to use for the calculation of the derivative of a function
 Formula for calculating the derivative of a function sum : (u+v)' = u'+v'
 Formula for calculating the derivative of a function product : (uv)' = u'v+uv'
 Formula for calculating the derivative of a function multiplied by a constant : (ku)' = ku'
 Formula for calculating the inverse derivative of a function : `(1/v)'` = `(v')/v^2`
 Formula for calculating the derivative of the ratio of two functions : `(u/v)'` = `(u'vuv')/v^2`
 Formula for calculating the derivative of the chain rule : `(u@v)'= v'*u'@v`
Table of derivatives of common functions
It is also necessary to know differentiated the usual functions which are in the following table (the differential calculator can help you) :
By applying these formulas and using this table, it is possible to calculate the derivative of any function.
These are the
calculation methods that the calculator uses to find the derivatives of functions.
Equation of the tangent to a curve at a point
C is the representative curve of a function f derivable at a point a.
The tangent to C at the point A(a;f(a)) is the straight line through A whose directing coefficient is `f'(a)`.
An
equation of the tangent to C at point A(a;f(a)) is :
`y = f(a) + f'(a)(xa)`.
Increasing and decreasing functions and differential calculus.
Let f be a differentiable function on an interval I.
 f is increasing on I if, and only if, its derivative is strictly positive for all x of I.
 f is decreasing on I if, and only if, its derivative is strictly negative for all x of I.
 f is constant on I if, and only if, its derivative cancels for all x of I.
Calculating the antiderivatives of a function
Formulas for calculating antiderivatives
The following conventions are used in the
antiderivative integral table: c represents a constant.
The calculator allows to obtain an antiderivative for many usual functions.
Real functions : calculators

abs : absolute value. The abs function calculates online the absolute value of a number.

antiderivative : indefinite integral calculator. The antiderivative calculator allows to calculate an antiderivative online with detail and calculation steps.

arccos : arccosine. The arccos function allows the calculation of the arc cosine of a number.
The arccos function is the inverse functions of the cosine function.

arcsin : arcsine. The arcsin function allows the calculation of the arc sine of a number.
The arcsin function is the inverse function of the sine function.

arctan : arctangent. The arctan function allows the calculation of the arctan of a number.
The arctan function is the inverse functions of the tangent function.

array_values : array of values of a function. The values calculator returns the table of values of a function obtained from an initial value and the difference between two consecutive values (steps).

ch : hyperbolic cosine. The function ch calculates online the hyperbolic cosine of a number.

cos : cosine. The cos trigonometric function calculates the cos of an angle in radians,
degrees or gradians.

cosec : cosecant. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.

cotan : cotangent. The cotan trigonometric function to calculate the cotan of an angle in radians,
degrees or gradians.

coth : hyperbolic cotangent. The coth function calculates online the hyperbolic cotangent of a number.

cube_root : cube root. The cube_root function calculates online the cube root of a number.

degree : degree of a polynomial. The degree function calculates online the degree of a polynomial.

derivative : derivative calculator. The derivative calculator allows steps by steps calculation of the derivative of a function with respect to a variable.

equation_solver : solve for x calculator. The equation solver allows to solve equations with an unknown with calculation steps : linear equation,
quadratic equation, logarithmic equation, differential equation.

exp : exponential. The function exp calculates online the exponential of a number.

inequality_solver : inequality calculator. Inequality solver that solves an inequality with the details of the calculation: linear inequality, quadratic inequality.

integral : integral calculator. The integral calculator calculates online the integral of a function between two values, the result is given in exact or approximated form.

is_odd_or_even_function : even or odd function calculator. Calculator for determining whether a function is an even function and an odd function.

limit : limit calculator. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps.

ln : napierian logarithm. The ln calculator allows to calculate online the natural logarithm of a number.

log : logarithm. The log function calculates the logarithm of a number online.

sec : secant. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.

sh : hyperbolic sine. The sh function allows to calculate online the hyperbolic sine of a number.

sin : sine. The sin trigonometric function to calculate the sin of an angle in radians,
degrees or gradians.

sqrt : square root. The sqrt function allows to calculate the square root of a number in exact form.

tan : tangent. The tan trigonometric function to calculate the tan of an angle in radians,
degrees or gradians.

taylor_series_expansion : Taylor expansion calculator. The taylor series calculator allows to calculate the Taylor expansion of a function.

th : hyperbolic tangent. The function th allows to calculate online the hyperbolic tangent of a number.

valuation : valuation of a polynomial. The valuation function allows to calculate the valuation of a polynomial online.
Real functions : games and quizzes
Real functions : exercises
 Exercise 1414, simplify the square root of an integer  square roots : The purpose of this corrected math exercise is to simplify the square root of an integer.
 Exercise 1415, solve a square equation  square roots  solving equations  equations : The purpose of this corrected math exercise is to solve an equation of the form `x^2=a`.
 Exercise 1416, simplifying a product of square roots  square roots : The purpose of this corrected math exercise is to simplify a product of square roots.
 Exercise 1417, simplifying a quotient of square roots  square roots : The purpose of this corrected math exercise is to simplify a quotient of square roots.
 Exercise 1418, simplifying a square root  square roots  order, absolute value, inequations  numbers and equations : The purpose of this corrected math exercise is to write a square root in a simplified form.
 Exercise 1419, simplifying a quotient of square roots  square roots : The purpose of this corrected math exercise is to write a quotient of square roots in a simplified form.
 Exercise 1435, calculating the value of a function for a given number  integers and rational numbers : The purpose of this corrected math exercise is to calculate the value of a function for a given number.
 Exercise 1505, even and odd functions  square and inverse functions : The purpose of this corrected exercise is to determine the parity of a function (specify whether the function is even or odd).
 Exercise 1506, determine the parity of a function from its graphical representation  square and inverse functions : The purpose of this corrected exercise is to determine graphically the parity of a function (specify whether the function is even or odd).
 Exercise 1507, graphical representation of the square and inverse functions  square and inverse functions : The aim of this corrected exercise is to recognize from their graphical representations the square and inverse functions.
 Exercise 1509, angle conversions  sine and cosine functions : The goal of this math exercise is to convert angles expressed in degrees into radians.
 Exercise 1510, trigonometric calculation  sine and cosine functions : The aim of this math exercise is to calculate expressions that contain sines, cosines and remarkable angles.
 Exercise 1511, absolute value of a numerical expression  order, absolute value, inequations : This corrected exercise consists simply in calculating the absolute value of a numerical expression.
 Exercise 1512, absolute value of a fraction  order, absolute value, inequations : This corrected exercise consists simply in calculating the absolute value of an algebraic expression composed of fractions.
 Exercise 1513, equation with absolute value  order, absolute value, inequations  equations : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form xa=b).
 Exercise 1514, equation with absolute value  order, absolute value, inequations  equations : The purpose of this corrected exercise is to solve an equation with an absolute value (equation of the form xa=b).
 Exercise 1604, derivative number of a function  derivatives of functions : The aim of this corrected maths exercise is to calculate the derivative number of a function.
 Exercise 1605, derivative of a polynomial  derivatives of functions : The purpose of this exercise is to determine through the methods of algebraic calculations the derivative of a polynomial function.
 Exercise 1606, derivative of a square root  derivatives of functions : The purpose of this corrected math exercise is to calculate the derivative of a square root.
 Exercise 1607, derivative of a quotient  derivatives of functions : The purpose of this corrected math exercise is to calculate the derivative of a quotient.
 Exercise 1608, derivative of a quotient and a polynomial  derivatives of functions : The purpose of this corrected math exercise is to calculate the derivative of a quotient and a polynomial.
 Exercise 1609, derivative of a polynomial and a square root  derivatives of functions : The goal of this corrected math exercise is to calculate the derivative of a polynomial and a square root.
 Exercise 1610, derivative of a function composed of a square root and a polynomial  derivatives of functions : The purpose of this corrected math exercise is to calculate the derivative of a function composed of a square root and a polynomial.
 Exercise 1611, derivative of a quotient of polynomials  derivatives of functions : The goal of this exercise on functions is to calculate the derivative of a quotient of polynomials.
 Exercise 1612, derivative of the product of a square root and a polynomial  derivatives of functions : The purpose of this exercise on functions is to calculate the derivative of the product of a square root and a polynomial.
 Exercise 1613, derivative and equation of the tangent  derivatives of functions : The purpose of this corrected math exercise is to calculate the derivative number of a function and derive the equation of a tangent to a curve.
 Exercise 1709, simplification of the neperian logarithm  neperian logarithm : The purpose of this corrected exercise is to simplify a neperian logarithm containing a power.
 Exercise 1710, simplifying the neperian logarithm of a quotient  neperian logarithm : The goal of this corrected exercise is to simplify a neperian logarithm containing a quotient.
 Exercise 1711, simplification of a fraction and the neperian logarithm of a quotient  neperian logarithm : The goal of this corrected exercise is to simplify the product of a fraction and a neperian logarithm containing a quotient.
 Exercise 1712, simplifying the neperian logarithm of a square root  neperian logarithm : The aim of this corrected exercise is to simplify the neperian logarithm of a square root.
 Exercise 1713, neperian logarithm and primitive calculation  neperian logarithm  antiderivatives : The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation.
 Exercise 1714, neperian logarithm and primitive calculation  neperian logarithm  antiderivatives : The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation.
 Exercise 1715, neperian logarithm and derivative calculation  neperian logarithm  derivatives of functions : The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.
 Exercise 1716, neperian logarithm and derivative calculation  neperian logarithm  derivatives of functions : The goal of this corrected exercise is to use the neperian logarithm to calculate the derivative.
 Exercise 1717, exponential and neperian logarithm  exponential : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.
 Exercise 1718, exponential and neperian logarithm  exponential : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.
 Exercise 1719, exponential and neperian logarithm  exponential : The goal of this corrected exercise is to use the properties of the exponential and the neperian logarithm to simplify an algebraic expression.
 Exercise 1731, exponential and derivative calculation  exponential  derivatives of functions : The aim of this corrected exercise is to use the exponential for the calculation of derivatives.
 Exercise 1740, calculation of the antiderivative of a polynomial function  antiderivatives : The goal of this corrected exercise is to calculate a function primitive.
 Exercise 14111, simplified writing of the sum of an integer and a square root  square roots : The objective of this exercise is to write an expression composed of the sum of an integer and a square root.
 Exercise 14112, simplification of a sum of square roots  square roots : The objective of this exercise is to simplify an expression composed of several square roots.
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