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The Derivative Calculator lets you calculate derivatives of functions online!
The calculator supports computing the first, second, … derivative as well as differentiating functions with many variables (partial derivatives).
With the Derivative Calculator you can check your solutions to calculus exercises. Even though it can show a step by step differentiation, it is not meant to be used for cheating!
For more about how to use the Derivative Calculator, go to "Help" or take a look at the examples.
Set differentiation variable and order in "Options". Check your input:
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Use parentheses, if necessary, or refer to the help.
Enter a formula into the Derivative Calculator above. Click "Go!" to calculate the derivative and display it.
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For those with a technical background, the following section explains how the Derivative Calculator works.
First, a parser analyzes the mathematical formula. 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 formulas 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 a LaTeX formula. MathJax takes care of displaying the formula in the browser.
When the "Go!" button is clicked, the Derivative Calculator sends the mathematical formula and the settings (differentiation variable and order) to the server, where it is analyzed again using the same JavaScript code (this is possible using node.js). This time, the formula 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 formula. Like any computer algebra system, it applies a number of rules to simplify the formula 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 rely 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 formula simplifications, are 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.
If you have any questions or ideas for improvements to the Derivative Calculator, don't hesitate to write me an e-mail.
© David Scherfgen 2012 — all rights reserved.
