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Text Content

DERIVATIVE CALCULATOR


CALCULATE DERIVATIVES ONLINE
— WITH STEPS AND GRAPHING!

Also check the Integral Calculator!
Calculadora de Derivadas en español
Ableitungsrechner auf Deutsch

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About
Help
Examples
Options
Practice

The Derivative Calculator lets you calculate derivatives of functions online —
for free!

Our calculator allows you to check your solutions to calculus exercises. It
helps you practice by showing you the full working (step by step
differentiation).

The Derivative Calculator supports computing first, second, …, fifth derivatives
as well as differentiating functions with many variables (partial derivatives),
implicit differentiation and calculating roots/zeros. You can also check your
answers! Interactive graphs/plots help visualize and better understand the
functions.

For more about how to use the Derivative Calculator, go to "Help" or take a look
at the examples.

And now: Happy differentiating!

Enter the function you want to differentiate into the Derivative Calculator.
Skip the "f(x) =" part! The Derivative Calculator will show you a graphical
version of your input while you type. Make sure that it shows exactly what you
want. Use parentheses, if necessary, e. g. "a/(b+c)".

In "Examples", you can see which functions are supported by the Derivative
Calculator and how to use them.

When you're done entering your function, click "Go!", and the Derivative
Calculator will show the result below.

In "Options" you can set the differentiation variable and the order (first,
second, … derivative). You can also choose whether to show the steps and enable
expression simplification.

Clicking an example enters it into the Derivative Calculator. Moving the mouse
over it shows the text.

$x^2 - \frac{1}{3}y + 0.7z$ $\alpha x^2+\beta x+\gamma$ $\frac{x}{x^2+1}$
$\operatorname{f}(x) \operatorname{f}'(x)$ $a_1x+K_\text{abc}$
$x^{-\frac{1}{3}}$ $\mathrm{e}^{1-x}$ $\sqrt{x}$ $\sqrt[3]{x+1}$ $\ln(x)$
$\log_{8}(x)$ $|x|$ $\sin(x)$ $\cos(x)$ $\tan(x)$ $\arcsin(x)$ $\arccos(x)$
$\arctan(x)$ $\sec(x)$ $\sinh(x)$ $\operatorname{arsinh}(x)$
$\operatorname{erf}(x)$ $\operatorname{B}(x,y)$ $\operatorname{\Gamma}(x)$
$\operatorname{Si}(x)$ $\mathrm{e}$ $\mathrm{\pi}$ $\mathrm{i}$

Configure the Derivative Calculator:

Differentiation variable: ax_____abcdfghjklmnopqrstuvwxyz Differentiate how many
times? 1 2 3 4 5 Simplify expressions? Simplify all roots?
(√x² becomes x, not |x|) Use complex domain (ℂ)? Keep decimals? Show calculation
steps? Calculate roots/zeros? Implicit differentiation? Dependent variable:
(will be treated as a function) ax_____abcdfghjklmnopqrstuvwxyz

The practice problem generator allows you to generate as many random exercises
as you want.

You find some configuration options and a proposed problem below. You can accept
it (then it's input into the calculator) or generate a new one.



Inverse trigonometric/hyperbolic functions Hyperbolic functions Cosecant, secant
and cotangent

Accept problem  Next problem


CALCULATE THE DERIVATIVE OF …ENTER YOUR OWN ANSWER:

Exit "check answer" mode
CLR + – × ÷ ^ √ ³√ π ( )

This will be calculated:

Loading … please wait!
This will take a few seconds.

ddx[sin(√ex+a2)]



Not what you mean? Use parentheses! Set differentiation variable and order in
"Options".


SUPPORT

Donate

Please support me if you like this page. Donate via PayPal to remove the ads.*

* Please choose to cover the PayPal fees. After donating, you will receive an
e-mail.



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RESULT

Above, enter the function to derive. Differentiation variable and more can be
changed in "Options". Click "Go!" to start the derivative calculation. The
result will be shown further below.

×

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HOW THE DERIVATIVE CALCULATOR WORKS

For those with a technical background, the following section explains how the
Derivative Calculator works.

First, a parser analyzes the mathematical function. It transforms it into a form
that is better understandable by a computer, namely a tree (see figure below).
In doing this, the Derivative Calculator has to respect the order of operations.
A specialty in mathematical expressions is that the multiplication sign can be
left out sometimes, for example we write "5x" instead of "5*x". The Derivative
Calculator has to detect these cases and insert the multiplication sign.

The parser is implemented in JavaScript, based on the Shunting-yard algorithm,
and can run directly in the browser. This allows for quick feedback while typing
by transforming the tree into LaTeX code. MathJax takes care of displaying it in
the browser.

When the "Go!" button is clicked, the Derivative Calculator sends the
mathematical function and the settings (differentiation variable and order) to
the server, where it is analyzed again. This time, the function gets transformed
into a form that can be understood by the computer algebra system Maxima.



Maxima takes care of actually computing the derivative of the mathematical
function. Like any computer algebra system, it applies a number of rules to
simplify the function and calculate the derivatives according to the commonly
known differentiation rules. Maxima's output is transformed to LaTeX again and
is then presented to the user.

Displaying the steps of calculation is a bit more involved, because the
Derivative Calculator can't completely depend on Maxima for this task. Instead,
the derivatives have to be calculated manually step by step. The rules of
differentiation (product rule, quotient rule, chain rule, …) have been
implemented in JavaScript code. There is also a table of derivative functions
for the trigonometric functions and the square root, logarithm and exponential
function. In each calculation step, one differentiation operation is carried out
or rewritten. For example, constant factors are pulled out of differentiation
operations and sums are split up (sum rule). This, and general simplifications,
is done by Maxima. For each calculated derivative, the LaTeX representations of
the resulting mathematical expressions are tagged in the HTML code so that
highlighting is possible.

The "Check answer" feature has to solve the difficult task of determining
whether two mathematical expressions are equivalent. Their difference is
computed and simplified as far as possible using Maxima. For example, this
involves writing trigonometric/hyperbolic functions in their exponential forms.
If it can be shown that the difference simplifies to zero, the task is solved.
Otherwise, a probabilistic algorithm is applied that evaluates and compares both
functions at randomly chosen places.

The interactive function graphs are computed in the browser and displayed within
a canvas element (HTML5). For each function to be graphed, the calculator
creates a JavaScript function, which is then evaluated in small steps in order
to draw the graph. While graphing, singularities (e. g. poles) are detected and
treated specially. The gesture control is implemented using Hammer.js.

If you have any questions or ideas for improvements to the Derivative
Calculator, don't hesitate to write me an e-mail.

© David Scherfgen 2023 — all rights reserved.

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Enter your function here. To calculate the derivative, click the "Go!" button.

www.derivative-calculator.net Open in urlscan Pro 176.9.19.242 Public Scan

Form analysis 1 forms found in the DOM

Text Content

www.derivative-calculator.net Open in urlscan Pro
176.9.19.242 Public Scan

Form analysis
1 forms found in the DOM