Logarithmic Differentiation Calculator

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

Logarithmic differentiation will provide a way to differentiate a function of this type. It requires deft algebra skills and careful use of the following unpopular, but well-known, properties of logarithms. Free Online Derivative Calculator allows you to solve first order and higher order derivatives, providing information you need to understand derivative concepts. Wolfram Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. In general, functions of the form y = f (x) g (x) work best for logarithmic differentiation, where: The functions f (x) and g (x) are differentiable functions of x. It’s easier to differentiate the natural logarithm rather than the function itself. The implicit differentiation calculator will find the first and second derivatives of an implicit function treating either `y` as a function of `x` or `x` as a function of `y`, with steps shown. The Derivative Calculator supports solving first, second., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. You can also get a better visual and understanding of the function by using our graphing tool. Chain Rule: d d x f (g (x)) = f '.

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)'.

Logarithmic Differentiation Calculator

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:

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.

Accept problemNext problem

Exit 'check answer' mode

This will be calculated:

Loading … please wait!
This will take a few seconds.

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

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How To Do Logarithmic Differentiation

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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.

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.

Implicit Differentiation Calculator

Calculator

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 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.

The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5). For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. While graphing, singularities (e. g. poles) are detected and treated specially. The gesture control is implemented using Hammer.js.

If you have any questions or ideas for improvements to the Derivative Calculator, don't hesitate to write me an e-mail.

The following variables and constants are reserved:

Logarithmic Differentiation Calculator Online

  • e = Euler's number, the base of the exponential function (2.718281...)
  • i = imaginary number (i² = -1)
  • pi, π = the ratio of a circle's circumference to its diameter (3.14159...)
  • phi, Φ = the golden ratio (1,6180...)

You can enter expressions the same way you see them in your math textbook. Implicit multiplication (5x = 5*x) is supported. If you are entering the derivative from a mobile phone, you can also use ** instead of ^ for exponents. The interface is specifically optimized for mobile phones and small screens.

Supported differentiation rules

  • Sum rule
  • Elementary power rule
  • Constant factor rule
  • Product rule (Leibniz rule)
  • Quotient rule
  • Chain rule
  • Inverse function rule
  • Logarithmic derivatives
  • Exponential functions
  • Trigonometric functions
Logarithmic Differentiation Calculator

Differentiation Calculator

Calculating your Solution...