Their difference is computed and simplified as far as possible using Maxima. The "Check answer" feature has to solve the difficult task of determining whether two mathematical expressions are equivalent. For each calculated derivative, the LaTeX representations of the resulting mathematical expressions are tagged in the HTML code so that highlighting is possible. This, and general simplifications, is done by Maxima. For example, constant factors are pulled out of differentiation operations and sums are split up (sum rule). In each calculation step, one differentiation operation is carried out or rewritten. There is also a table of derivative functions for the trigonometric functions and the square root, logarithm and exponential function. The rules of differentiation (product rule, quotient rule, chain rule, …) have been implemented in JavaScript code. Instead, the derivatives have to be calculated manually step by step. Maxima's output is transformed to LaTeX again and is then presented to the user.ĭisplaying the steps of calculation is a bit more involved, because the Derivative Calculator can't completely depend on Maxima for this task. Like any computer algebra system, it applies a number of rules to simplify the function and calculate the derivatives according to the commonly known differentiation rules. Maxima takes care of actually computing the derivative of the mathematical function. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima. When the "Go!" button is clicked, the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server, where it is analyzed again. MathJax takes care of displaying it in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. The Derivative Calculator has to detect these cases and insert the multiplication sign. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". In doing this, the Derivative Calculator has to respect the order of operations. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). An improper fraction is a fraction where the numerator (top number is greater than or equal to the denominator (bottom number).For those with a technical background, the following section explains how the Derivative Calculator works.įirst, a parser analyzes the mathematical function. Improper fraction button is used to change a number of the form of 1 4/5 to the form of 9/5. A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number). Proper fraction button is used to change a number of the form of 9/5 to the form of 1 4/5. When you choose the one the other is switched off. Proper fraction button and Improper fraction button work as pair. If the fraction of decimal is part of a calculation, omit clicking equals and continue with the calculation. Click the fraction format button, enter a decimal, click equals and then click on a fraction form and then click equals. Also to change a decimal of the form 0.5 to the fraction 1/2, or change a decimal of the form 1.75 to a mixed number of the form 1 3/4 or to the fraction 7/4, or a fraction of the form 7/4 to the mixed number 1 3/4. 3/4 DEC x 6 =.įraction format button is used to work with all fractions. If the fraction or mixed number is only part of the calculation then omit clicking equals and continue with the calculation per usual. Click on the decimal format button, enter a fraction or mixed number, then click equals. Also to change a fraction of the form 3/4 to the decimal 0.75, or a fraction of the form 7/4 or a mixed number of the form 1 3/4 to the decimal 1.75. Decimal format button is used for all decimal work. Space, click another number and then click on the fraction bar button, lastly enter another number.ĭecimal format button and Fraction format button work as pair. You can use fraction space button to create a number of the form 5 3/4. Click a number and then click fraction bar, then click another number.
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