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). If those slopes are equal, then the lines are found to be parallel.For those with a technical background, the following section explains how the Derivative Calculator works.įirst, a parser analyzes the mathematical function. Using those coordinate points, calculate the slope of each line. Two determine if two lines on a graph are parallel, first, find two coordinate points on each of the lines. In other words, the slopes of these lines are either equal or opposite.įor example, two lines both with the slope 3/4 would be parallel, but also a line with the slope 3/4 and the slope -3/-4 would also be parallel since even though they are headed in opposite directions, they would never cross paths when extended to infinity. Parallel lines are defined as any set of two or more lines that when extended to infinity, would never cross paths. X2 is any x coordinate on the parallel lineįrom these two equations, the slope-intercept form of the parallel line can be found and would equal:.y2 is any y coordinate on the parallel line.
Where b is the y-intercept in the parallel line.Where m1 is the slope of the first line.The following formulas are used to calculate a parallel line. Enter the slope-intercept form of the first equation, and a coordinate point the second line passes through to calculate the equation of the second line.
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