Derivative Of Arctanx/3
What Is The Derivative Of Arctan

The Derivative Calculator supports computing first, second, fifth derivatives as well as differentiating functions with many variables (partial derivatives), implicit differentiation and calculating roots/zeros. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions. Derivative of arctan(x) Let’s use our formula for the derivative of an inverse function to ﬁnd the deriva tive of the inverse of the tangent function: y = tan−1 x = arctan x. We simplify the equation by taking the tangent of both sides: y = tan−1 x tan y = tan(tan−1 x) tan y = x.

Derivative Of Inverse Tangent. The following are the formulas for the derivatives of the inverse trigonometric functions. We let y=arctan x. Using implicit differentiation and solving for dy/dx: derivative of tany. Derivative of x. Therefore, 1+tan2y. Substituting x=tany in from above. Derivative of arctan. What is the derivative of the arctangent function of x? The derivative of the arctangent function of x is equal to 1 divided by (1+x 2).

The Derivative Calculator lets you calculate derivatives of functions online — for free!

Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step differentiation).

The Derivative Calculator supports computing first, second, …, fifth derivatives as well as differentiating functions with many variables (partial derivatives), implicit differentiation and calculating roots/zeros. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions.

For more about how to use the Derivative Calculator, go to 'Help' or take a look at the examples.

And now: Happy differentiating!

Enter the function you want to differentiate into the Derivative Calculator. Skip the 'f(x) =' part! The Derivative Calculator will show you a graphical version of your input while you type. Make sure that it shows exactly what you want. Use parentheses, if necessary, e. g. 'a/(b+c)'.

In 'Examples', you can see which functions are supported by the Derivative Calculator and how to use them.

When you're done entering your function, click 'Go!', and the Derivative Calculator will show the result below.

In 'Options' you can set the differentiation variable and the order (first, second, … derivative). You can also choose whether to show the steps and enable expression simplification.

Clicking an example enters it into the Derivative Calculator. Moving the mouse over it shows the text.

Configure the Derivative Calculator:

Differentiation variable:
Differentiate how many times?
Simplify expressions?
Simplify all roots? (√x² becomes x, not \|x\|)
Use complex domain (ℂ)?
Keep decimals?
Show calculation steps?
Calculate roots/zeros?
Implicit differentiation?
Dependent variable: (will be treated as a function)

The practice problem generator allows you to generate as many random exercises as you want.

You find some configuration options and a proposed problem below. You can accept it (then it's input into the calculator) or generate a new one.

Inverse trigonometric/hyperbolic functions
Hyperbolic functions
Cosecant, secant and cotangent

Accept problemNext problem

Calculate the Derivative of …Enter your own Answer:

Exit 'check answer' mode

This will be calculated:

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This will take a few seconds.

Not what you mean? Use parentheses! Set differentiation variable and order in 'Options'.

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Result

Above, enter the function to derive. Differentiation variable and more can be changed in 'Options'. Click 'Go!' to start the derivative calculation. The result will be shown further below.

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 function. 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 expressions 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 LaTeX code. MathJax takes care of displaying it in the browser.

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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. This time, the function gets transformed into a form that can be understood by the computer algebra systemMaxima.

Maxima takes care of actually computing the derivative of the mathematical function. 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'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 depend 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 simplifications, is 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.

The 'Check answer' feature has t

Derivative Of Arctan