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). This is your inverse function.For those with a technical background, the following section explains how the Derivative Calculator works.įirst, a parser analyzes the mathematical function. The final equation should be (1-cbrt(x))/2=y.
These steps are: (1) take the cube root of both sides to get cbrt(x)=1-2y (2) Subtract 1 from both sides to get cbrt(x)-1=-2y (3) Divide both sides by -2 to get (cbrt(x)-1)/-2=y (4) simplify the negative sign on the left to get (1-cbrt(x))/2=y.
#Inverse equation calculator series#
Now perform a series of inverse algebraic steps to solve for y. Then invert it by switching x and y, to give x=(1-2y)^3. First, set the expression you have given equal to y, so the equation is y=(1-2x)^3. Nevertheless, basic algebra allows you to find the inverse of this particular type of equation, because it is already in the "perfect cube" form. Your question presents a cubic equation (exponent =3). The article is about quadratic equations, which implies that the highest exponent is 2. For the inverse function, now, these values switch, and the domain is all values x≥5, and the range is all values of y≥2.įirst, let me point out that this question is beyond the scope of this particular article. Recall that for the original function the domain was defined as all values of x≥2, and the range was defined as all values y≥5. Compare the domain and range of the inverse to the domain and range of the original.Therefore, the correct solution for the inverse function is the positive option. Recall that you originally defined the domain as x≥2, in order to be able to find the inverse function. Using that as the domain, the resulting values of y (the range) are either all values y≥2, if you take the positive solution of the square root, or y≤2 if you select the negative solution of the square root. Therefore, allowable values of x (the domain) must be x≥5. Look for a function in the form of y = a x 2 + c must always be positive.
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