# Calculus calculators: Multivariable Calculus Calculator

## Calculus Calculator & Solver – SnapXam

### Get detailed solutions to your math problems with our

Calculus step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

1

2

3

4

5

6

7

8

9

a

b

c

d

f

g

m

n

u

v

w

x

y

z

.

(◻)

+

×

◻/◻

/

÷

2

√◻

√◻

e

π

ln

log

log

lim

d/dx

Dx

|◻|

θ

=

>

<

>=

<=

sin

cos

tan

cot

sec

csc

asin

acos

atan

acot

asec

acsc

sinh

cosh

tanh

coth

sech

csch

asinh

acosh

atanh

acoth

asech

acsch

Example

Solved Problems

Difficult Problems

1

Solved example of calculus

$\int\cos\left(3x\right)\cdotd\cdot x\cdot dx$

2

We can solve the integral $\int\cos\left(3x\right)dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let’s call it $u$), which when substituted makes the integral easier. We see that $3x$ it’s a good candidate for substitution. Let’s define a variable $u$ and assign it to the choosen part

$u=3x$

Intermediate steps

Differentiate both sides of the equation $u=3x$

$du=\frac{d}{dx}\left(3x\right)$

Find the derivative

$\frac{d}{dx}\left(3x\right)$

The derivative of the linear function times a constant, is equal to the constant

$3$

3

Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. We need to calculate $du$, we can do that by deriving the equation above

$du=3dx$

4

Isolate $dx$ in the previous equation

$\frac{du}{3}=dx$

5

Substituting $u$ and $dx$ in the integral and simplify

$\int\frac{\cos\left(u\right)}{3}du$

Intermediate steps

Take the constant $\frac{1}{3}$ out of the integral

$\frac{1}{3}\int\cos\left(u\right)du$

Divide $1$ by $3$

$\frac{1}{3}\int\cos\left(u\right)du$

6

Take the constant $\frac{1}{3}$ out of the integral

$\frac{1}{3}\int\cos\left(u\right)du$

7

Apply the integral of the cosine function: $\int\cos(x)dx=\sin(x)$

$\frac{1}{3}\sin\left(u\right)$

Intermediate steps

$\frac{1}{3}\sin\left(3x\right)$

8

Replace $u$ with the value that we assigned to it in the beginning: $3x$

$\frac{1}{3}\sin\left(3x\right)$

9

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{1}{3}\sin\left(3x\right)+C_0$

$\frac{1}{3}\sin\left(3x\right)+C_0$

#### Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!

## Derivative Calculator: Wolfram|Alpha

WolframAlpha

ddx xsin

x2

Math Input

Calculus & Sums

### More than just an online derivative solver

Wolfram|Alpha is a great calculator for first, second and third derivatives; derivatives at a point; and partial derivatives. 2 x) wrt x

• View more examples »

### Access instant learning tools

Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator

• Step-by-step solutions »
• Wolfram Problem Generator »

### What are derivatives?

#### The derivative is an important tool in calculus that represents an infinitesimal change in a function with respect to one of its variables.

Given a function , there are many ways to denote the derivative of with respect to . The most common ways are and . When a derivative is taken times, the notation or is used. These are called higher-order derivatives. Note for second-order derivatives, the notation is often used.

At a point , the derivative is defined to be . This limit is not guaranteed to exist, but if it does, is said to be differentiable at . Geometrically speaking, is the slope of the tangent line of at .

As an example, if , then and then we can compute : . The derivative is a powerful tool with many applications. For example, it is used to find local/global extrema, find inflection points, solve optimization problems and describe the motion of objects.

### How Wolfram|Alpha calculates derivatives

Wolfram|Alpha calls Wolfram Languages’s D function, which uses a table of identities much larger than one would find in a standard calculus textbook. It uses well-known rules such as the linearity of the derivative, product rule, power rule, chain rule and so on. Additionally, D uses lesser-known rules to calculate the derivative of a wide array of special functions. For higher-order derivatives, certain rules, like the general Leibniz product rule, can speed up calculations.

## All online calculators

 Luhn algorithm Calculates the checksum of a sequence of digits using the Luhn algorithm, calculates a check digit (a digit that can be added to the original sequence to get a sequence with a checksum ending in 0).  Antilog Antilog calculator. Single Variable Function Approximation The calculator uses regression methods to approximate a single variable function. Roman numeral arithmetic Calculator supporting basic mathematical operations (addition, subtraction, multiplication and division) on integers represented by Roman numerals. Fast exponentiation modulo The calculator raises large numbers to a power modulo The probability that a certain number of events will occur when multiple trials are run. Bernoulli trials. Using the Bernoulli formula, calculates the probability of multiple events occurring. The table and graph of the binomial distribution function shows the probability of all possible cases. Coprime and pairwise coprime This calculator checks if the entered numbers are coprime and pairwise coprime. The validation rule is described below the calculator.  Expression of length in different units The calculator expresses the given length in different units. Evaluation of expressions with multiple variables The calculator calculates the value of a mathematical expression with multiple variables. Derivative calculation by its definition This online calculator performs numerical differentiation – an approximate calculation of the derivative of a function at a given point. The method of transition to the limit by successive approximations is used until the specified accuracy is reached. Calculate partial derivative by definition This online calculator performs numerical differentiation of a function of several variables – an approximate calculation of all partial derivatives of a function at a given point – with respect to all variables. Normally distributed random number generator The calculator generates a given number of normally distributed random numbers using the Box-Muller transform on uniformly distributed random numbers obtained from the built-in Javascript random number generator.  Number Sequence Generator The calculator generates a sequence of numbers falling out of a given range. For example, the order in which the kegs are drawn in the loto is numbers from 1 to 90 will be listed randomly, or a “5 out of 36” lottery. Random Matrix Generator This online calculator generates a random matrix with given parameters. BCD The calculator converts a number from decimal to binary, but written in packed BCD, and vice versa. Complement of This online calculator calculates the complement of the number and the complement of the reduced base number for the given number system Factorial fractions This online calculator calculates the result of division when both the numerator and denominator contain the factorial of the number Egyptian fractions fraction. Egyptian numbers The calculator displays numbers as a set of ancient Egyptian hieroglyphs.  Barrel and bucket problem How to draw a certain volume of water from a barrel using buckets of different sizes? Write Mathematical Expressions Contains a calculator with examples of writing mathematical expressions. Golden section Calculation of lengths of segments in the golden section. Egyptian fraction to rational number Calculator converts Egyptian fraction to fraction Lagrange interpolation polynomial (Lagrange polynomial) This online calculator builds interpol rational Lagrange polynomial for a given set of points. The calculator also plots both the Lagrange polynomial and the basic polynomials, interpolates given points, and shows a step-by-step solution. Newton’s interpolation polynomial (Newton’s polynomial) This online calculator generates a Newton’s interpolation polynomial for a given set of points.  The calculator shows a step-by-step solution, interpolates given points, and plots. Covariance This online calculator calculates the covariance or correlation moment for two discrete random variables Root and power of Raising to an arbitrary power, extracting the root of an arbitrary degree. Linear Recurrence Sequence This online calculator calculates a given number of members of a linear recurrence sequence (return sequence) and also displays their sum in cumulative total. Linear Diophantine equations in two variables Calculator solves linear Diophantine equations in two variables. Malthusian Growth Model Given initial parameters, this online calculator plots the Malthusian growth model, also known as the exponential law. Cramer’s method with detailed solution Calculator for solving systems of linear equations by Cramer’s method.  A detailed solution is given – the calculator displays all intermediate matrices and determinant values. Runge-Kutta method This online calculator implements the classical Runge-Kutta method (also known as the Runge-Kutta method) of the fourth order of accuracy. The method is used to solve differential equations of the first degree with a given initial value Euler method This online calculator implements the Euler method, a numerical method for solving differential equations of the first degree of the first order of accuracy. Iteration method (method of successive approximations) Finding the roots of functional equations by iterations (successive approximations). Verhulst model This online calculator plots the Verhulst-Pearl equation, or logistic curve, using given initial parameters. Greatest common divisor (gcd) of two integers This calculator finds the greatest common divisor (gcd) of two integers using the Euclidean algorithm.  Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of several numbers This calculator finds the greatest common divisor (GCD) and least common multiple (LCM) of two or more integers by factoring numbers into prime factors. The description of the algorithm can be found under the calculator. Least common multiple and greatest common divisor of two integers Find the greatest common divisor (GCD) and least common multiple (LCM) of two integers. Least common denominator of two or more fractions Find the lowest common denominator of two or more fractions. Continued fraction The calculator represents a common fraction as a continued fraction. Normal Distribution Plots the probability density and distribution density functions for the normal distribution. Inverse matrix Finding the inverse matrix using the union matrix.  Inverse matrix modulo Finding the inverse of a matrix modulo using the union matrix and the inverse element in the ring modulo. Olympiad tasks Calculators that solve several Olympiad problems in mathematics. Matrix rank determination Matrix rank calculator Matrix determinant Matrix determinant calculation by definition. Gaussian matrix determinant Finding the matrix determinant by converting the matrix to a triangular form. Works in rational and complex numbers Remainder of division The calculator gives the remainder of the division of two whole (or fractional) numbers. Conversion of the measure of an angle from the hour system to the degree system and from the degree system to the hour The article contains two calculators, the first one is designed to convert the angle from the hour measure to the degree measure, the second – from the degree measure to the hour measure Calculation of the sum and product of numbers corresponding to the letters in the word Numerological calculator at the request of the user.  Finding missing numbers This calculator can be used to find gaps in a sequence of numbers. Search for prime numbers. Sieve of Eratosthenes. The calculator finds prime numbers using an algorithm known as the “Sieve of Eratosthenes” Reduction of a matrix to a triangular form Reduction of a matrix to a triangular form by the Gauss method and the Bareis method. Derivative of exponential function The function is raised to the power of itself a specified number of times and then the derivative is taken. Proportion Calculates an unknown proportion term. Created at the request of the user. Decomposition of a square matrix into symmetric and skew-symmetric matrices This online calculator represents a square matrix as the sum of a symmetric and a skew matrix. Student’s t-distribution Calculates the value of the distribution function and probability density for the Student’s t-distribution.  Calculates Student’s quantiles for a given number of degrees of freedom and a given probability. Levenshtein distance Calculator for calculating the Levenshtein distance between two words. Calculation of the helix Calculation of unknown helix dimensions from known dimensions. Spiral parameters: outer diameter, inner diameter, thickness (spiral pitch), spiral length, number of turns. Extended Euclid’s algorithm Calculator that implements the extended Euclid’s algorithm. Resultant The calculator calculates the resultant of two polynomials. The Sylvester matrix is ​​also displayed. Problem solving The calculator displays and calculates the values ​​of the missing variables from the given formulas and input parameters. Arithmetic progression problem solving This online calculator helps to solve some types of arithmetic progression problems Geometric progression problem solving This online calculator helps to solve some types of geometric progression problems 90 007 Solution of the canonical linear programming problem by the simplex method Solution of the canonical linear programming problem by the single-phase simplex method.  Solving quadratic equations Quadratic equations are equations of the form axx+bx+c=0. For example, 4xx+2x+1=0. Such equations are solved in terms of the discriminant. This calculator will help you quickly calculate the value of a quadratic equation. Just first bring it to the above form. For example, from 5xx-2x-0=0 to 5xx+(-2x)+0=0, from 3xx=0 to 3xx+0x+0=0. Solving an inhomogeneous system of linear algebraic equations by the matrix method Solving an inhomogeneous system of linear algebraic equations (SLAE) by the matrix method (method of solving through the inverse matrix). Solving a system of linear algebraic equations by the Gauss method The calculator solves a system of linear algebraic equations given as a matrix by the Gauss method. A step by step solution is given. Solving a system of linear algebraic equations by the Gaussian method, preserving fractions The calculator solves a system of linear algebraic equations, given in the form of a matrix, using the Gaussian method, preserving fractions throughout the process.  At the end, the result is given both as a real number and as a fraction with a numerator and a denominator. Solving a system of linear equations by the Gaussian method with finding a general solution Solve a system of linear algebraic equations by the Gaussian method. Knows how to derive a solution for joint indefinite systems of linear equations. It also outputs the result in floating point and fraction format. Solving a system of non-linear equations This online calculator attempts to find a solution to a system of non-linear equations using a coordinate search method. Solving comparisons modulo This calculator solves linear comparisons, or comparisons of the first degree modulo m polynomials Relationships between two numbers All kinds of relationships between two numbers. Created at the request of the user. Standard form of a number Converts a number to the standard form – the product of the mantissa from 1 to 10 and the exponent of the number 10.  metic progression up to the indicated number, as well as a series, representing the sums of the sums of the progression. Sum of numbers This online calculator will help you calculate the sum of numbers written one after another. Bernoulli Table of Independent Trials This online calculator calculates the probability k of success when performing n repeated independent trials with a given probability of success p (Bernoulli scheme), for k varying from zero to n. Bayes Theorem This online calculator calculates the posterior probabilities of events according to Bayes Theorem Miller-Rabin Primality Test The calculator checks whether a number is composite using the Miller-Rabin test. Fermat’s primality test Performs a primality test based on Fermat’s little theorem with given reasons. Matrix transposition Matrix transposition, what else can I say.  Matrix multiplication The calculator multiplies two matrices. Malthus equation This online calculator calculates the unknown parameter of the Malthusian equation from known parameters. Equation of a straight line from two points This online calculator finds the formulas of the parametric equation of a straight line and the equation of a straight line with a slope coefficient using the coordinates of two points belonging to a straight line. Factorial This online calculator calculates the factorial of a positive integer. Pretty much any positive integer – it’s only limited by the amount of time you’re willing to spend to wait for the calculation to finish. For example, I waited for the result of calculating the factorial of 100,000! Integer factorization. Divisor enumeration Factorization of integers by enumeration of divisors. The distribution function of a discrete random variable The distribution function of a random variable is used to describe systems, present experimental data in an analytical form for statistical analysis.  Centered moving average This calculator calculates a centered moving average for a given averaging period Aztec Numbers The calculator converts positive integers to the Aztec number form. Maya numerals Calculator converts the number to the Maya number system Numerical puzzles – replacing numbers with letters Solver of numerical puzzles. Numerical or mathematical puzzles are mathematical expressions in which all or part of the numbers are replaced by some symbols, such as letters. It is required to replace each character with the desired number in order for the expression to be true.

## Integrals Calculator • Step by step!

#### Support

At the top of the page, enter the function you want to integrate. Integration variable , integration limits and other parameters can be changed in section “ Settings “. Press “ = ” to start integration/antiderivative. The result will be shown below on this page.

#### How the Integral Calculator works

For those who are interested in the technical details, this section describes how the Integrals Calculator works and works.

First, the parser analyzes the original mathematical expression. It converts it into a form more convenient for the computer, namely into the form of a tree (see the picture below). In the process of such transformation, the Integral Calculator must respect the order of operations, taking into account their priority. As well as the fact that in mathematical expressions the multiplication sign is often omitted, for example, we usually write “5x” instead of “5*x”. An integral calculator should be able to understand such cases and add the multiplication sign itself.

The parser is written in JavaScript and is based on the marshalling yard algorithm, so it can be executed directly in the browser. This makes it possible to generate a human-readable expression on the fly, converting the resulting tree into code for LaTeX (LaTeX). With the help of MathJax, the image is generated and displayed in the browser.

On pressing the “=” button, the Integral Calculator sends the mathematical expression along with the parameters (integration variable and integration limits) to the server, where it is analyzed again. This time, the expression is converted into a form that will be understood by the computer algebra system Maxima (Maxima).

Maxima calculates the integral of a mathematical function. Maxima’s result is again converted to LaTeX and then shown to the user. The antiderivative is calculated using the Risch algorithm, which is quite sophisticated for human understanding. That is why the task of showing intermediate steps for solving integrals is so difficult.

In order to still show a step-by-step solution, the Integral Calculator uses the same methods that a person would use. The algorithm that does this was developed over several years and was written in Maxima’s own programming language. The program contains more than 17,000 lines of code. If the expression to be integrated has the same form as a known one, the algorithm applies predefined rules for solving the integral (for example, the method of indefinite coefficients for rational functions, trigonometric substitution in square root integrals of a quadratic function, or integration by parts for products of certain functions). If it does not coincide with the already known, then the algorithm tries different substitutions and transformations until the integral is solved or until the time allotted for this ends, or until all possible options run out. On the one hand, the Calculator does not have mathematical intuition, which would be of great help in the search for an antiderivative, but, on the other hand, the Calculator is able to try a large number of different options in a very short time. Such a step-by-step calculation of the antiderivative according to the rules is often more compact and elegant than that calculated by Maxima. Another “Check Solution” mode of operation is to solve the complex problem of determining whether two mathematical expressions are equal to each other. The difference between the expressions is calculated and simplified using the Maxima as much as possible. For example, it could be rewriting trigonometric/hyperbolic functions into their exponential forms. If it is possible to simplify the difference to zero, the task is completed. Otherwise, a probabilistic algorithm is applied that evaluates and compares both expressions at random locations. In the case of the antiderivative, the whole procedure is repeated for each derivative, since the antiderivative may differ by a constant.

Interactive function graphs are computed in the browser and rendered on canvas from HTML5. For each math function that needs to be drawn, the Calculator creates a JavaScript function, which is then calculated in increments necessary to display the graph correctly. All singularities (e.g. poles) of a function are detected during rendering and handled separately. 