The Derivative Calculator lets you calculate derivatives of features online — because that free!

Our calculator permits you to inspect your services to calculus exercises. It helps you practice by reflecting you the full working (step by step differentiation).

You are watching: Derivative of ln x 2 1

The Derivative Calculator supports computing first, second, …, fifth derivatives and also differentiating features with countless variables (partial derivatives), latent differentiation and calculating roots/zeros. Friend can additionally check your answers! interactive graphs/plots aid visualize and much better understand the functions.

For more about exactly how to usage the Derivative Calculator, walk to "Help" or take a look at the examples.

And now: Happy differentiating!

Enter the role you want to distinguish into the Derivative Calculator. Skip the "f(x) =" part! The Derivative Calculator will display you a graphical variation of her input while you type. Make certain that it mirrors exactly what girlfriend want. Use parentheses, if necessary, e.g. "a/(b+c)".

In "Examples", you have the right to see which attributes are supported by the Derivative Calculator and also how to use them.

When you"re excellent entering her function, click "Go!", and the Derivative Calculator will present the an outcome below.

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

Clicking an instance enters it into the Derivative Calculator. Moving the computer mouse over it mirrors the text.

$x^2 - frac13y + 0.7z$$alpha x^2+eta x+gamma$$fracxx^2+1$$a(x^2+b)$$a_1x+K_ extabc$$x^-frac13$$mathrme^1-x$$sqrtx$$sqrt<7>x+1$$ln(x)$$log_8(x)$$|x|$$sin(x)$$cos(x)$$ an(x)$$arcsin(x)$$arccos(x)$$arctan(x)$$sec(x)$$sinh(x)$$operatornamearsinh(x)$$operatornameerf(x)$$operatornameB(x,y)$$operatornameGamma(x)$$operatornameSi(x)$$mathrme$$mathrmpi$$mathrmi$

Configure the Derivative Calculator:

Differentiation variable:Differentiate how many times?Simplify expressions?Simplify all roots?(√x² becomes x, no |x|)Use complex domain (ℂ)?Keep decimals?Show calculate steps?Calculate roots/zeros?Implicit differentiation?Dependent variable:(will it is in treated as a function)

The practice trouble generator enables you to create as countless random exercises together you want.

You find some configuration alternatives and a proposed trouble below. You have the right to accept that (then it"s input into the calculator) or create a brand-new one.

Inverse trigonometric/hyperbolic functionsHyperbolic functionsCosecant, secant and also cotangent
Accept problemNext problem

Calculate the Derivative of …Enter your own Answer:

Exit "check answer" mode


This will be calculated:


Loading … you re welcome wait!This will certainly take a few seconds.

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

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Above, go into the role to derive. Differentiation variable and an ext can be readjusted in "Options". Click "Go!" to start the derivative calculation. The an outcome will be shown further below.

How the Derivative Calculator Works

For those through a technical background, the adhering to section explains how the Derivative Calculator works.

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

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

When the "Go!" switch is clicked, the Derivative Calculator sends out the mathematical function and the setups (differentiation variable and also order) to the server, whereby it is analyzed again. This time, the role gets transformed into a form that have the right to be construed by the computer system algebra device Maxima.


Maxima takes care of actually computing the derivative of the mathematical function. Like any type of computer algebra system, it uses 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 also is then presented to the user.

Displaying the steps of calculate is a bit much more involved, since the Derivative Calculator can"t totally depend ~ above Maxima because that this task. Instead, the derivatives need to be calculated manually step by step. The rule of differentiation (product rule, quotient rule, chain rule, …) have been imposed in JavaScript code. There is likewise a table the derivative attributes for the trigonometric functions and also the square root, logarithm and exponential function. In each calculation step, one differentiation procedure is brought out or rewritten. For example, constant factors room pulled out of differentiation operations and also sums are split up (sum rule). This, and also general simplifications, is done by Maxima. Because that each calculation derivative, the LaTeX representations of the resulting mathematical expressions are tagged in the HTML code so that highlighting is possible.

The "Checkanswer" function has to fix the an overwhelming task of determining whether two mathematical expressions space equivalent. Their difference is computed and simplified as much as feasible using Maxima. Because that example, this entails writing trigonometric/hyperbolic attributes in your exponential forms. If it can be shown that the distinction simplifies come zero, the task is solved. Otherwise, a probability algorithm is applied that evaluates and also compares both features at randomly liked places.

The interactive role graphs are computed in the browser and displayed in ~ a canvas aspect (HTML5). Because that each role to be graphed, the calculator create a JavaScript function, i beg your pardon is then evaluated in tiny steps in stimulate to draw the graph. If graphing, singularities (e.g. Poles) room detected and also treated specially. The gesture control is enforced using Hammer.js.

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If girlfriend have any questions or ideas for enhancements to the Derivative Calculator, don"t hesitate to create me one e-mail.