This will be calculated:
Not what you mean? Use parentheses! Set differentiation variable and order in "Options".
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 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.
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.
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.
If you have any questions or ideas for improvements to the Derivative Calculator, don't hesitate to write me an e-mail.