## Introduction to Fourth Derivative Calculator

The fourth order derivative calculator is an online tool that calculates the fourth derivative of a function. It is a free online differentiation calculator that calculates the rate of change of a function while doing some simple clicks. For this, it just requires an input function and the respected variable.

Calculus is based on two significant concepts of derivatives and integration. And the derivatives involve the rate of change of a quantity with respect to another. Sometimes you need to calculate the rate of change of a function up to four times which is a lengthy and tricky process. Therefore, we introduce you to an online tool that can help you calculate derivatives easily.

## Formula used by Fourth Order Derivative Calculator

The fourth derivative calculator uses the derivative formula and provides a smart way to calculate the rate of change of a function. It is made to calculate derivatives up to the fourth order.

Since the fourth derivative of a function tells the sudden rate of change in a function, this calculator tells you how a function can suddenly increase or decrease. For this, it uses the following formula.

$f'(x)=\lim_{x\to0}\frac{f(x+\delta x)-f(x)}{\delta x}{2}lt;/p>

For the fourth order derivative,

$f''''(x)=\frac{d^4y}{dx^4}{2}lt;/p>

The derivative of a function helps to find out the slope of a curved line calculator which also tells the rate of change in the function. Our advanced math calculator uses the above formula to find out a solution without doing any manual calculations.

## Fourth Derivative Example

Let's calculate the fourth derivative of e^-2x. For this assume that,

$y=e^{-2}{2}lt;/p>

Differentiating both sides with respect to x,

$\frac{dy}{dx}=\frac{d}{dx}(e^{-2x}){2}lt;/p>

Since the derivative of an exponential function is itself an exponential function, therefore,

$\frac{dy}{dx}=-2e^{-2x}{2}lt;/p>

Hence the first derivative of e-2x is -2e-2x. But we need to calculate fourth derivative. Therefore, we will differentiate e^-2x four times. Now, by differentiating the first derivative of e^-2x, we get

$\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}(-2e^{-2x}){2}lt;/p>

$\frac{d^2y}{dx^2}=-2(-2)e^{-2}=4e^{-2x}{2}lt;/p>

Similarly, the third derivative of e^-2x will be

$\frac{d^3y}{dx^3}=4(-2)e^{-2}=-8e^{-2x}{2}lt;/p>

Now the differentiation of the thrid e^(-2x) derivative again will give the fourth derivative. That is,

$\frac{d^4y}{dx^4}=-8(-2)e^{-2x}=16e^{-2x}{2}lt;/p>

## How to find Fourth Degree Derivative Calculator?

The derivative calculator offers many online tools to assist you in learning more about derivatives. One of these tools is the fourth order derivative calculator that you can easily find online. To find this calculator online, use the following steps.

- Use the main keywords to find the tool in the browser of your choice.
- You'll get different results from your search engine. You can select the fourth implicit derivative calculator based on these results.
- On the website page, there will be a list of derivative tools.

Select the desired tool from the list. Or you can also use our different tools, such as the extreme point calculator that helps you to calculate maximum and minimum points.

## How does the Fourth Order Derivative Calculator work?

The 4th order derivative calculator works on the provided input function. It uses the fundamental differentiation formula to find rate of instantaneous change in the function. It provides you a step-by-step complete solution of fourth derivative by differentiate a function four times.

When you provide an input function to the derivative calculator, it first analyzes the function and then differentiate it four times. Although the calculation of four order derivatives is a lengthy procedure, our derivative tool provides you with a quick and accurate solution.

## Why to use Fourth Derivative Calculator?

The main goal of determining a fourth order derivative is to examine the sudden rate of change with respect to its independent variable. Also, you can determine the rate of change of function by using a derivative graph calculator. This calculator assists you in determining how a function suddenly changes.

While doing calculations for the fourth-order derivative, you may get stuck due to incorrect calculations because the calculations for the fourth are tricky and long-term. The fourth order derivative calculator may help you find the 4th derivative without doing any long-term calculations. Therefore, it would be best for you to calculate the fourth derivative by using the product rule calculator.

## Benefits of using Fourth Order Derivative Calculator

This calculator has many benefits that you can get by using it online. Some of these are listed below;

- It is easy to use because you must perform only a few simple steps.
- It provides an easy step-by-step solution to get the fourth derivative without manual calculations.
- It is a free online tool, so you don’t have to pay for other premium tools.
- It provides you with 100% accurate and quick results.
- You can learn more about using this calculator. You can also learn to calculate the fourth derivative of a function by using the chain rule.

## How to use the 4th Derivative Calculator?

Using this online calculator to calculate the rate of change of a function a second or fourth time is a quick and easy way. It requires input values to do calculations. Use the following steps to use this calculator.

- 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 four times.
- Now select the variable by which you want to differentiate the given function.
- Review the function and click the calculate button.

After Clicking the calculate button, you will get the solution within a few seconds. You can also calculate the rate of change of a function at a specific point by derivative at a point calculator.

## Frequently asked questions

### What does the 4th derivative tell you?

The fourth order derivative of a function tells you the sudden rate of change at some specific points. It tells you the rate of change in the “jerk” part of acceleration i.e. those moments when the acceleration suddenly speeds up such as a lift or elevator ascending quickly.

### How do you find the fourth derivative?

It is extremely easy to find a second, third, fourth, or higher derivative. A function's second derivative is simply its first derivative's derivative. The third derivative is a derivative of the second derivative. The fourth derivative is the derivative of the third, and so on.

### What do 2nd derivatives tell us?

The second derivative of a function tells the rate of change of its first derivative. And the sign with the second derivative explains whether the slope of the tangent line is increasing or decreasing.

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