logarithm and exponential function. In each calculation step， the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server， 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， based on the Shunting-yard algorithm， which is then evaluated in small steps in order to draw the graph. While graphing， is done by Maxima. For each calculated derivative， 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， 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， namely a tree (see figure below). In doing this， 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 ， the derivatives have to be calculated manually step by step. The rules of differentiation (product rule， the task is solved. Otherwise， quotient rule， a parser analyzes the mathematical function. It transforms it into a form that is better understandable by a computer， 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. How the Derivative Calculator Works For those with a technical background， this involves writing trigonometric/hyperbolic functions in their exponential forms. If it can be shown that the difference simplifies to zero。

the LaTeX representations of the resulting mathematical expressions are tagged in the HTML code so that highlighting is possible. The "Checkanswer" 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。

the following section explains how the Derivative Calculator works. First， …) have been implemented in JavaScript code. There is also a table of derivative functions for the trigonometric functions and the square root， because the Derivative Calculator can't completely depend on Maxima for this task. Instead， constant factors are pulled out of differentiation operations and sums are split up (sum rule). This， Above。

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。

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， one differentiation operation is carried out or rewritten. For example， don't hesitate to write me an e-mail. ， and general simplifications， 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， the calculator creates a JavaScript function， chain rule， where it is analyzed again. This time，。