## Introduction to Quotient Rule Calculator

Quotient Rule Calculator with steps is an online tool to evaluate the derivative of a function in fractional form. It uses the quotient rule to find the derivative for problems where one function is divided by another.

In mathematics, using an online tool is an innovative and efficient way of learning. There is always a need to find a tool that makes the learning procedure easy. Here we introduce application software online that is made on this concept. It covers the needs of students who struggle in mathematics.

## What is a Quotient Calculator?

Quotient Rule Derivative Calculator with steps is a tool online that facilitates the students and mathematicians using internet connectivity. It comprises the quotient rule of derivative, which follows all other rules like the power rule, product rule, etc.

Derivative Quotient Rule Calculator differentiates the ratio of two functions step by step. So you can understand the concept easily. It provides all possible actions of the calculations. That’s why using this calculator helps improve your mathematical skills.

## How to use Quotient Rule Derivative Calculator?

Every tool works on the given input. Online Quotient Calculator uses the fractional function as an input. There are simple steps to use this tool online. These are:

- You need to enter the function in the “Enter Function” box in the first step. Then review the value of the function bellowed.
- Secondly, choose the variable from the “With Respect to” box.
- In the third step, click on the ‘Calculate” button.

This tool will start processing the given input as you click on the calculate button. After a few moments, it will show the results with all possible steps.

## Formula used by Quotient Rule Online Calculator

The concept of derivative is used to calculate the rate of change of a function with respect to an independent variable such as ‘x’. Similarly the quotient rule is a rule of derivative that is used to calculate the rate of change of a function given in fractional form.

Let $$ y \;=\; \frac{f(x)}{g(x)} $$ is a function to be differentiated. The derivative of this function can be calculated as:

$$ \frac{dy}{dx} \;=\; \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) \;=\; \Biggr[\frac{f(x)}{g(x)}\Biggr]' $$In more generalized form,

$$ \frac{dy}{dx} \;=\; \frac{g(x) \;.\; f'(x) \;-\; f(x) \;.\; g'(x)} {\{g(x)\}^2} $$Quotient Rule Calculator uses this formula to differentiate mathematical problems.

A solution of an example is given below to see how to use this formula manually.

**Example:**

Find the derivative of

$$ y \;=\; \frac{e^x}{x^2} $$
**Solution:**

Since the given function is in fractional form, we will use the quotient formula to solve it.

$$ y \;=\; \frac{e^x}{x^2} $$Apply the derivative formula on both sides with respect to ‘x’.

$$ \frac{dy}{dx} \;=\; \frac{d}{dx} \Biggr[ \frac{e^x}{x^2}\Biggr] $$ $$ \frac{dy}{dx} \;=\; \frac{x^2 \;.\; e^x \;-\; e^x \;.\; 2x}{(x^2)^2} $$The required solution is,

$$ \frac{dy}{dx} \;=\; \frac{x^2.e^x \;-\; 2x.e^x}{x^4} $$## Why to use Derivative Quotient Rule Calculator?

One of the main reasons to use the Online Quotient Rule Calculator is that it provides a step-by-step solution that is helpful to understand it. Because by manual calculation, you can’t focus on understanding the concept. It allows you to solve different examples quickly.

In mathematics, the calculus course has many exciting but confusing concepts. Students always feel a need for external help in different forms. But the requirement of an online tool is much rather than other resources. The Quotient Derivative Rule Calculator facilitates the students and helps them by solving different examples.

One exciting thing about the quotient rule is that it is similar to the product rule. So, there are a lot of chances that you may confuse them and may use the product rule instead of the quotient rule. That’s why you need to use Derivative using the Quotient Rule Calculator.

## Benefits of using Online Quotient Rule Calculator

The use of an online derivative tool improves mathematical skills. Some of the significant benefits of this calculator are:

- It saves you time that you may surf in manual calculations.
- Quotient Rule Calculator with steps provides the solution in an action by step manner.
- It provides all possible steps and intermediate stages of the solution to make it easy to understand.
- You can also review the problem graphically because this tool plots a graph according to the solution.
- Finding the Derivative using Quotient Rule Calculator is easy to use because it assists you with already given examples.
- Since the product and quotient rules of the derivatives are very similar, that cannot be very clear for you. Quotient Derivative Calculator saves from confusion between these two rules.
- It is an efficient and accurate tool because there are no chances of mistakes in the solution as it verifies the result by integrating it.
- It improves your problem solving skills by solving different examples.
- The Quotient Rule Derivative Calculator can easily find a given function's global maximum and local minimum value.
- You don't have to pay any fee to use this tool.