## Introduction to Sixth Derivative Calculator

The sixth order derivative calculator is an online tool with which you can differentiate a function six times in a single step. It makes the calculations of derivatives easier for you. It requires only an input function and the variable with which the function is to be differentiated.

The two fundamental concepts of calculus, i.e. derivative and integration help to deal with the continuous rate of change. These two concepts are important not only in mathematics but also in different fields of science.

We introduce you to an online tool that assists you to calculate the sixth derivative of a function. It is mostly helpful in physics where you want to differentiate a position vector with respect to time. You can also use our fourth derivative calculator that gives you the sudden rate of change in any function.

## Formula used by Sixth Order Derivative Calculator

The sixth derivative of a function is calculated by applying a derivative on the fourth derivative. In other words, it is necessary to calculate all derivatives of the function up to the 5th order to find the sixth derivative.

Like the fifth order derivative calculator, the 6ht derivative calculator also uses the differentiation formula. It is expressed as;

$f'(x)=\lim_{x\to0}\frac{f(x+\delta x)-f(x)}{\delta x}$

Where, the rate of change in f(x) is calculated as f'(x). Sometimes, it also refers to the slope of a curved line. It is because it calculates the rate of change at a specific point on the curved line.

The above formula in terms of sixth derivative is,

$f''''''(x)=\frac{d^6y}{dx^6}$

The calculation of the sixth derivative is simple and easy by using this calculator.

## Example of sixth derivative

To calculate the sixth derivative of e^2x, assume that,

$y=e^{2x}$

Differentiating both sides with respect to x.

$\frac{dy}{dx}=\frac{d}{dx}(e^{2x})$

Since $\frac{dy}{dx}$ is also referred to the first derivative of e^2x so it can be written as y_1, therefore,

$y_1=2e^{2x}$

To find the 6th derivative, we need to differentiate e^2x six times. Now differentiating again with respect to x, we get,

$\frac{d}{dx}(y_1)=y_2=\frac{d}{dx}(2e^{2x})$

$y_2=4e^{2x}$

Similarly, the Third derivative of e^2x is,

$y_3=\frac{d}{dx}(4e^{2x})=8e^{2x}$

Similarly, 4th derivative can be calculated by differentiating 3rd derivative of e^2x with respect to x which is,

$y_4=16e^{2x}$

The 5th derivative of e^2x is,

$y_5=32e^{2x}$

Similarly, the sixth derivative of e^2x is obtained by differentiating the 5th derivative with respect to x,

$y_6=\frac{d}{dx}(32e^{2x})=64e^{2x}$

## How to find the sixth derivative calculator online?

You can find this tool by using your search engine easily. For this, you can use the following steps.

- Open your desired browser such as chrome or mozilla firefox and navigate to the search engine google.
- Now search for a sixth derivative calculator. You will get a list of different websites of derivative tools.
- Review the list of different websites and choose the 6th order derivative calculator

## How does the 6th derivative calculator work?

Since every tool works only when an input is provided. Similarly, this tool also works when you provide an input function to it. It uses the derivative formula in the backend to find the 6th derivative of a function. It provides you the 6th derivative of a function by applying the derivative formula six times, which is a lengthy procedure. But our tool completes this process within a few seconds after collecting input functions from you.

When you input a function in this tool, it analyzes the function. It identifies that either the function is differentiable or not. If the function is differentiable, then it provides you the calculations of the 6th derivative step-by-step. Our advanced tool is also capable of providing a visual representation of the given function. Therefore, you can also visualize the change in a function at every point.

## Why to use the 6th Derivative Calculator?

Derivatives have many applications in physics and other different fields of science. The higher order derivative helps to model real-life problems. For this, you can use our sixth order derivative calculator. It provides you a smart and easy way to find derivatives.

While computing higher order derivatives of a function, you have to find out all derivatives one-by-one. But it is a lengthy and tricky process and a small error results in an incorrect solution. Therefore, it would be best for you to use this calculator that can help you to avoid long-term manual calculations.

## Benefits of using Sixth Derivative Calculator

This calculator has numerous benefits of being used to do calculations and for knowledge purposes. Some of these benefits are listed below.

- It is easy to use because you just need to follow some simple steps to use it.
- It provides you with the calculations of the sixth derivative with a 100% accurate solution.
- It is free to use so you don't have to pay to use premium tools.
- It saves you from long-term calculations of derivatives, so you can learn more in less time.
- You can do practice with different examples again and again like a physical calculator.
- It uses all derivative rules to provide you a quick solution.

## How to use Sixth Derivative Calculator with steps?

It is a smart way to use this tool to calculate the sixth derivative. It is because you can do calculations by following some simple steps. These steps are;

- In the first step, you need to enter the function. This step requires a function for which you want to calculate the rate of change six times.
- Now select the variable by which you want to differentiate the given function.
- Review the function and click the calculate button.

Within a few seconds of pressing the calculate button, this calculator will give you the precise answer. Additionally, the derivative graph will be shown so you can see the rate of change graphically.

## Frequently Asked Questions

### What is the 6th derivative called?

Pop is a name that has been given to the derivative of a position vector 6th times with respect to time. The rate at which crackle changes over time is known as the amplitude.

### How do you find the sixth derivative?

First of all you calculate the previous 5 derivatives one-by-one, then calculate the sixth derivative of a function. In other words, calculate the 5th derivative which is the derivative of 4th derivative.

### What is an nth derivative?

The term nth derivative describes any of the higher order derivatives of a function. The first derivative is obtained by taking a single derivative of a function. You get the second derivative by differentiating the new function a second time.

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