# Quotient Rule Calculator

quotient-rule-calculator

## Introduction to the Quotient Rule Derivative Calculator

The quotient rule calculator with steps is an online available tool that is based on the quotient rule for finding derivatives. It is used for finding the derivative of the given function in other forms such as fractional form.

The derivative calculator quotient rule is a freely available tool that provides free and accurate results to its users.

The quotient derivative calculator is lightning-fast, saving users time. Likewise, our chain rule derivative calculator simplifies complex differentiation tasks for efficient math solutions.

## What is the Quotient Derivative Calculator?

A quotient rule calculator is a smart tool for finding the derivatives using the quotient rule. The Quotient rule derivative calculator is used for the functions that are in the fractional form.

This tool eases the life of students, mathematicians, engineers, and other related people by doing one-click calculations.

The quotient of two functions calculator is for functions divided by one another, while our differentiate using product rule calculator specializes in finding derivatives for functions multiplied together. Each calculator comes with step-by-step instructions to simplify your calculus tasks.

## Formula used by Quotient Rule Calculator

The formula that is used by this Derivative Quotient Rule Calculator is based on the quotient rule for finding the derivative. This derivative calculator quotient rule is based on the method of evaluating the function that is the ratio of two differential functions.

Mathematically,

$$\frac{d}{dx} \left[ \frac{f(x)}{g(x)} \right] \;=\; \frac{g(x)f'(x)-f(x)g'(x)}{[g(x)^2]}$$

Let's see how this formula helps to calculate derivatives in the below example:

Example: Differentiate the following function using the Quotient rule of derivatives.

$$y \;=\; \frac{x^2}{x+1}$$

Solution: Differentiate the function w.r.t "x"

$$\frac{d}{dx}(y) \;=\; \frac{d}{dx} \left[ \frac{x^2}{x+1} \right]$$

By using the above-mentioned formula for quotient rule of derivatives,

$$\frac{dy}{dx} \;=\; \frac{ (1+x) \frac{d}{dx}(x^2) - x^2 \frac{d}{dx}(1+x)} {(1+x)^2}$$ $$\frac{dy}{dx} \;=\; \frac{ 2x(1+x) - x^2 } {(1+x)^2}$$ $$\frac{dy}{dx} \;=\; \frac{ x(x+2) } {(1+x)^2}$$

And thats it is...

In the same way, our calculators provide step-by-step instructions. For equations with hidden relationships, explore our implicit derivative calculator for effortless solutions.

## How does Quotient Rule Calculator with Steps Work?

To find the Quotient rule calculator, usually following steps are performed to calculate the rational functions:

Step 1: First of all, Enter all the values in the required input fields. Like, enter the function, variables, and all other additional values.

Step 2: You can load the example from the drop-down list of examples.

Step 3: Now, select the variable w.r.t to which you wish to differentiate the function.

Step 4: After entering all the values in the required fields, just click on the “Calculate” button. The quotient rule derivative calculator will evaluate the differential functions.

Finally, the differentiation of the given differential function will be displayed on your screen. After evaluating the function, refresh the page for new calculations. If you want to visualize the derivative graph, explore our derivative plotter for a graphical representation of the results.

## How to Find the Derivative Quotient Rule Calculator?

Following are the methods to get this calculator online from any search engine like Google, Yandex, Bing or any other you are using.

1. First of all, if you are a regular user of this website you can directly search the URL of this calculator. Also you can bookmark this derivative online tools website for accesing them at any time.
2. Secondly, you can search this calculator using keywords on SERP as "quotient rule calculator" or "quotient derivative calculator".

Choose any of these methods and just start your calculations right now.

Related: Master derivatives with our Quotient Rule Calculator, and you can also expand your calculus skills with our free second order derivative calculator.

## Advantages of Quotient of Two Functions Calculator

Following is the list of benefits while using this quotient rule calculator with the steps listed below:

• The derivative quotient rule calculator is a totally free and easily available tool.
• This online tool is error-free and doesn’t charge any subscriptions from their users. This calculator has free unlimited access that the user can do calculations multiple times.
• This tool gives error-free results.
• This quotient of two functions calculator makes calculations easier for students, scientists, and engineers.
• The user interface of this online tool is very friendly.
• This calculator gives you results in a fraction of a second.
• The quotient derivative calculator gives the solution with step-by-step instructions.

Note: Keep the math momentum going! Visit our other derivative solver to tackle various problems with ease. Math made simple, right at your fingertips.

### What is the Quotient Rule

The quotient rule is a helpful rule of calculus that helps to calculate the derivative of the quotient rule of the two functions. The quotient rule solver is also used to do so.

For example, if there are two functions f(x) (numerator) and g(x) (denominator) then quotient rule would be,

$$\biggr( \frac{f}{g} \biggr)’ \;=\; \frac{f’.g - f.g’}{(g)^2}$$

### What is the Quotient Rule for Exponents

The quotient rule for exponents is a special case that occurs in quotient rule. The quotient rule for exponents applies while dealing with exponential functions. It is specifically used to determine the derivative of the quotient of two functions when one or both functions are exponential.

The quotient rule differentiation calculator solves with respect to function. For example, if u(x) and v(x) is the differentiated functions of x then the derivative of the quotient rule is,

$$\biggr( \frac{u}{v} \biggr)’ \;=\; \frac{u’v - uv’}{(v)^2}$$

But if one function or both functions are exponential of the form ax then the qoutient rule will be,

$$\biggr( \frac{a^x}{v(x)} \biggr)’ \;=\; \frac{ln \; a.^x . v(x) - a^x . v’ (x)}{(v(x))^2}$$

### What is the Quotient Rule in Algebra

The quotient rule in algebra is used to simplify the expression that involves fractions or quotients. The quotient rule in algebra states that “to divide one fraction by another, you can multiply the first fraction by the reciprocal of the second fraction.

The quotient calculator solves according to the function. For example, if there are two fractions a/b and c/d then the quotient rule in algebra is,

$$\frac{ \frac{a}{b}}{\frac{c}{d}} \;=\; \frac{a}{b} \times \frac{d}{c}$$

### How would you Use the Quotient Rule to Find Given that g(x)

The derivative quotient calculator finds the g(x) by using the quotient rule, you can follow some steps

• Firstly, apply the quotient rule,

$$\frac{d}{dx} \biggr( \frac{f(x)}{g(x)} \biggr) \;=\; \frac{f’(x). g(x) - f(x) . g’(x)}{g(x))^2$$

• Now differentiate the numerator functions f(x)
• Differentiate the denominator function g(x)
• Apply the quotient rule formula on the derivatives f’(x) and g’(x) and substitute.
• Now simplify the above expression

### How to Differentiate Functions Using the Quotient Rule

The quotient rule could be used to differentiate functions in quotient law calculator and for differentiating functions follow the steps,

• Firstly, identify the numerator function f(x) and the denominator function g(x)
• Apply the quotient rule formula,

$$\frac{d}{dx} \biggr( \frac{f(x)}{g(x)} \biggr) \;=\; \frac{f’(x). g(x) - f(x). g’(x)}{(g(x))^2}$$

• Now calculate the derivative of the numerator function
• Determine the derivative of denominator function
• Apply the quotient rule formula in it
• Simplify the expression and analyze the results.