Derivative Calculator

This intuitive tool allows you to easily calculate the derivatives of common mathematical functions, helping you swiftly solve your math problems. Just enter your data below to get started.

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Online Derivative Calculator

This tool calculates the derivative of a function online. Common functions are accepted: sine, cosine, tangent, logarithm (log), exponential, square root, etc. (See table below).

Importance and Usage of Derivatives in Mathematics

The derivative of a function is a fundamental concept in mathematics, crucial in various fields such as engineering, physics, economics, and even in biological sciences. It allows us to measure how one quantity changes in response to a change in another quantity. In practice, this means understanding the rate of change, like the speed of a moving object or the growth rate of a population.

This online derivative calculator is designed to simplify and speed up the derivation process, making mathematical analysis more accessible and understandable, whether for students, teachers, or professionals. With this tool, it is possible to quickly obtain the derivatives of complex functions, thus facilitating the study and application of mathematical concepts in real life.

How to Use the Calculator

The procedure to use this calculator is simple and intuitive. Here are the steps to follow:

Enter the main variable (e.g., `x`).
Input the function to be derived (e.g., `x^2+x+1`).

Usage Example

Here are some examples to illustrate how to use the calculator:

To calculate the derivative of `f(x) = x^2`, enter `x` as the variable, `x^2` as the function.
To calculate the derivative of the function `f(x) = sin(x)`, enter `x`, `sin(x)` respectively.

Data Entry Guide

Variables	A function can have one or more variables, but only one main variable. A variable is a single lowercase or uppercase letter. Examples: A function f with one main variable : f(x) = 4x A function g with one main variable x and a secondary parameter m, g(x) = 4x*m + x + 1, In this case, enter x in the “main variable” field
Numbers	Use a dot as decimal separator
Operators	+ (addition), - (substration), * (multiplication), / (division), ^ (power), For multiply operator, enter ab not a.b nor ab. Example: 2x.
Constants	You may use these constants : pi (approx. 3.14), e (approx. 2,72) Examples: f(x) = pi * x or f(x) = e * (x+1+2*e)²
Common Functions	You may use theses functions in the expression of f(x) sqrt(x) (square root), exp(x) (exponential function), log(x) or ln (natural logarithm),
Trigonometric functions	You may use theses functions in the expression of f(x) sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), csc (cosecant),
Inverse trigonometric functions	You may use theses functions in the expression of f(x) arcsin (arcsine), arccos (arccosine), arctan (arctangent), arccot (arcotangent), arcsec (arcsecant), arccsc (arccosecant),
Hyperbolic Functions	You may use theses functions in the expression of f(x) sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), coth (hyperbolic cotangent), sech (hyperbolic secante), csch (hyperbolic cosecant)
Inverse hyperbolic functions	You may use theses functions in the expression of f(x) asinh (inverse hyperbolic sine), acosh (inverse hyperbolic cosine), atanh (inverse hyperbolic tangent), acoth (inverse hyperbolic cotangent), asech (inverse hyperbolic secant), acsch (inverse hyperbolic cosecant)

Table of basic derivatives

Fonction f(x)	Dérivée
`k` where `k in RR`	`0`
`x^n` where `n in NN`*	`n*x^(n-1)`
`1/x`	`-1/x^2`
`1/x^n` where `n in NN , n >=2`	`-n/x^(n+1)+C`
`sqrt(x)`	`1/(2*sqrt(x))`
`1/sqrt(x)`	`-1/(2xsqrt(x))`
`sin(x)`	`cos(x)`
`cos(x)`	`-sin(x)`
`ln(x)`	`1/x`
`e^x`	`e^x`

Table of composite functions derivatives

Fonction composée	Dérivée
`u^n` where `n in NN\text{ and }n >= -1`	`nu'u^(n-1)`
`1/u`	`-1/u^2+C`
`1/u^n` where `n in NN\text{ and }n >= 1`	`-(n*u')/u^(n+1)`
`sqrt(u)`	`(u')/(2*sqrt(u))`
`ln(\|u\|)`	`(u')/u`
`u^a` where `u > 0\text{ and } a in RR`	`au'u^(a-1)`
`e^u`	`u'*e^u`
`k*u \text{ where } k in RR`	`k*u'`
`u+v`	`u'+v'`
`u*v`	`u'v+uv'`
`u/v`	`(u'v-uv')/v^2`
`u @ v`	`v'*u' @ v`

Conclusion

This online derivative calculator is a powerful and intuitive tool, designed to make complex mathematical calculations more accessible and easier to understand. Whether you are a student, teacher, or professional, this tool offers a quick and effective way to calculate derivatives, helping you deepen your understanding of mathematical concepts and apply them effectively in your studies or work. We encourage you to try it and explore the vast possibilities it offers for your learning and practice of mathematics.