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

Our calculator enables you to check your services to calculus exercises. It helps you practice by showing you the complete working (step by action differentiation).

You are watching: Derivative of e^1/x

The Derivative Calculator supports computing first, second, …, fifth derivatives and differentiating functions with plenty of variables (partial derivatives), implicitly differentiation and also calculating roots/zeros. Friend can additionally check her answers! interaction graphs/plots aid visualize and far better understand the functions.

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

And now: Happy differentiating!

Enter the role you desire 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 sure that it shows exactly what girlfriend want. Usage parentheses, if necessary, e.g. "a/(b+c)".

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

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

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

Clicking an example enters it right into the Derivative Calculator. Relocating the 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 numerous times?Simplify expressions?Simplify every 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 together a function)

The practice problem generator permits you to generate as countless random exercises together you want.

You find some configuration alternatives and a proposed problem below. You can accept it (then it"s input into the calculator) or create a brand-new one.

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

Calculate the Derivative that …Enter your very own Answer:

Exit "check answer" mode


This will be calculated:


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

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

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Above, enter the role to derive. Differentiation variable and more can be changed in "Options". Click "Go!" to begin the derivative calculation. The an outcome will be presented further below.

How the Derivative Calculator Works

For those through a technological background, the following section describes how the Derivative Calculator works.

First, a parser analyzes the mathematics function. The transforms it into a type that is far better understandable by a computer, namely a tree (see number below). In act this, the Derivative Calculator needs to respect the bespeak of operations. A specialty in mathematical expression is the the multiplication sign deserve to be left the end sometimes, for example we create "5x" rather of "5*x". The Derivative Calculator needs to detect these cases and also insert the multiplication sign.

The parser is applied in JavaScript, based upon the Shunting-yard algorithm, and can run directly in the browser. This enables for fast feedback while inputting by transforming the tree into LaTeX code. MathJax takes treatment of displaying the in the browser.

When the "Go!" switch is clicked, the Derivative Calculator sends the mathematical role and the settings (differentiation variable and order) come the server, wherein it is analyzed again. This time, the role gets transformed into a type that deserve to be understood by the computer algebra device Maxima.


Maxima takes care of actually computer the derivative that the mathematical function. Like any kind of computer algebra system, it uses a number of rules to simplify the function and calculation the derivatives according to the generally known differentiation rules. Maxima"s output is changed to LaTeX again and is then presented come the user.

Displaying the procedures of calculation is a bit much more involved, because the Derivative Calculator can"t completely depend on Maxima for this task. Instead, the derivatives need to be calculated manually action by step. The rule of differentiation (product rule, quotient rule, chain rule, …) have actually been enforced in JavaScript code. There is likewise a table of derivative functions for the trigonometric functions and the square root, logarithm and also exponential function. In each calculation step, one differentiation procedure is carried out or rewritten. For example, consistent factors are pulled the end of differentiation operations and also sums are split up (sum rule). This, and also general simplifications, is excellent by Maxima. Because that each calculation derivative, the LaTeX depictions of the result mathematical expressions are tagged in the HTML password so that highlighting is possible.

The "Checkanswer" attribute has to settle the difficult task of determining whether two mathematical expressions are equivalent. Their difference is computed and also simplified as far as feasible using Maxima. Because that example, this entails writing trigonometric/hyperbolic functions in their exponential forms. If it have the right to be shown that the difference simplifies come zero, the task is solved. Otherwise, a probability algorithm is used that evaluates and also compares both features at randomly favored places.

The interactive role graphs space computed in the browser and also displayed in ~ a canvas facet (HTML5). For each duty to be graphed, the calculator creates a JavaScript function, i m sorry is climate evaluated in small steps in order to draw the graph. When graphing, singularities (e.g. Poles) space detected and treated specially. The gesture regulate is implemented using Hammer.js.

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If friend have any type of questions or principles for improvements to the Derivative Calculator, don"t hesitate to compose me one e-mail.