derivative calculator

Derivative calculator : How to use it?

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

Syntax :

derivative(function;variable), function is the function to differentiate
It is also possible to use the Leibniz notation, using the symbol $d/dx$

Examples :

derivative(sin(x)+x) $=1+cos(x)$
derivative(2x) $=2$
derivative(x^2) $=2*x$

The derivative calculator allows to do symbolic differentiation using the derivation property on one hand and the derivatives of the other usual functions. Derivative calculation obtained is returned after being simplified, with calculation steps.

With this derivative calculator, you can find :

Derivatives of polynomials online
Common derivative
Derivatives of sums
Differentiation of differences
Derivatives of product
Chain rule of derivatives
Step by step derivative

Derivatives of polynomials calculation online

The derivative calculator may calculate online the derivative of any polynomial.

For example, to calculate online the derivative of the polynomial following $x^3+3x+1$ , just enter derivative(x^3+3x+1), after calculating result $3*x^2+3$ is returned.

Calculate online common derivative

Derivative calculator is able to calculate online all common derivatives : sin, cos, tan, ln, exp, sh, th, sqrt (square root) and many more ...

Thus, to obtain the derivative of the cosine function with respect to the variable x, you must enter derivative(cos(x);x), result $-sin(x)$ is returned after calculation.

Calculate online derivatives of sums

The derivative of a sum is the sum of the derivatives, calculator uses this property to differentiate functions.

To calculate online the derivative of a sum, simply type the mathematical expression that contains the sum, specify the variable and apply derivative function.

For example, to calculate online the derivative of the sum of the following functions $cos(x)+sin(x)$ with the differentiation calculator online, enter derivative(cos(x)+sin(x);x), after calculating result $cos(x)-sin(x)$ is returned.

Calculating the derivative of $cos(x)+sin(x)$ with respect to x

Applying the formula $(u+v)'=u'+v'$ , with $u=cos(x)$ , $v=sin(x)$ , $u'=-sin(x)$ , v $'=cos(x)$

Calculating the derivative of $cos(x)$ with respect to x

This is a usual derivative.
The derivative of $cos(x)$ respect to x is equal to $-sin(x)$

Calculating the derivative of $sin(x)$ with respect to x

This is a usual derivative.
The derivative of $sin(x)$ respect to x is equal to $cos(x)$

So u'= $-sin(x)$ , v'= $cos(x)$ , substituting we obtain
The derivative of $cos(x)+sin(x)$ respect to x is equal to $-sin(x)+cos(x)$

Note that steps of the calculations for obtaining the calculation of the derivative are also displayed by the function.

Differentiation of differences

The differentiation calculator is able to do many calculations online : to calculate online the derivative of a difference, simply type the mathematical expression that contains the difference, specify the variable and apply derivative function.

For example, to calculate online the derivative of the difference of the following functions $cos(x)-2x$ , enter derivative(cos(x)-2x;x), after calculating result $-sin(x)-2$ is returned.

It is noted that description and steps calculations of the derivative are also displayed by the function.

Calculate online derivatives of product

To calculate online the derivative of a product, just input the mathematical expression that contains the product, specify the variable and apply derivative function.

For example, to calculate online the derivative of the product of the following functions $x^2*cos(x)$ , with the differentiate calculator enter derivative(x^2*cos(x);x), after calculating result $2*x*cos(x)-x^2*sin(x)$ is returned.

Note that there also the derivative is calculated online with the description and the steps of the calculations.

Calculate chain rule of derivatives

To calculate chain rule of derivatives, just input the mathematical expression that contains chain rule, specify the variable and apply derivative function.

To calculate the derivative of the chain rule, the calculator uses the following formula : $(f@g)'=g'*f'@g$

For example, to calculate online the derivative of the chain rule of the following functions $cos(x^2)$ , enter derivative(cos(x^2);x), after calculating result $-2*x*sin(x^2)$ is returned.

Note that there also the derivative is calculated online with the description and the steps of the calculations.

Calculating the derivative of $cos(x^2)$ with respect to x

Applying the chain rules: $f(g(x))=g'(x)*f'(g(x))$

Calculating the derivative of $cos(x^2)$ with respect to x^2

This is a usual derivative.
The derivative of $cos(x^2)$ respect to x^2 is equal to $-sin(x^2)$

Calculating the derivative of $x^2$ with respect to x

Applying the formula $(u^n)'=n*u'*u^(n-1)$ with $u=x$ , $n=2$

Calculating the derivative of $x$ with respect to x

The derivative of $x$ respect to x is equal to $1$

The derivative of $x^2$ respect to x is equal to $2*x$

The derivative of $cos(x^2)$ respect to x is equal to $2*x*(-sin(x^2))$

How to calculate a derivative?

To differentiate a function, it is necessary to know the following calculation rules and formulas:

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 : $(u/v)'$ = $(u'v-uv')/v^2$
Formula for calculating the derivative of the chain rule : $(u@v)'= v'*u'@v$

It is also necessary to know differentiated the usual functions which are in the following table (the differential calculator can help you) :

**Table of derivatives of common functions**
Derivative of k;x	$0$
Derivative of x	$1$
Derivative of x^n	$n*x^(n-1)$
Derivative of 1/x	$-1/x^2$
Derivative of 1/x^2	$-2/x^3$
Derivative of 1/x^n	$-n/x^(n+1)$
Derivative of sqrt(x)	$1/(2*sqrt(x))$
Derivative of abs(x)	$1$
Derivative of arccos(x)	$-1/sqrt(1-(x)^2)$
Derivative of arcsin(x)	$1/sqrt(1-(x)^2)$
Derivative of arctan(x)	$1/sqrt(1-(x)^2)$
Derivative of ch(x)	$sh(x)$
Derivative of cos(x)	$-sin(x)$
Derivative of cotan(x)	$-1/sin(x)^2$
Derivative of coth(x)	$-1/(sh(x))^2$
Derivative of exp(x)	$exp(x)$
Derivative of ln(x)	$1/(x)$
Derivative of log(x)	$1/(ln(10)*x)$
Derivative of sh(x)	$ch(x)$
Derivative of sin(x)	$cos(x)$
Derivative of tan(x)	$1/cos(x)^2$
Derivative of th(x)	$1/(ch(x))^2$

By applying the derivation formulas and using the usual derivation table, it is possible to calculate any function derivative. These are the calculation methods used by the calc to find the derivatives.

Games and quizzes on the calculation of the derivative of a function

To practice the different calculation techniques, several quizzes on the calculation of the derivative of a function are proposed.