## Introduction to Fifth Derivative Calculator

The fifth order derivative calculator is an online tool that you can use to calculate the derivative of a function up to 5th order. It provides a quick way to do calculations online and saves time and energy from the manual calculations of derivatives. It is based on the fundamental calculus concept of instantaneous rate of change.

In calculus, the derivative is an important concept. It deals with the study of the continuous rate of change. Every order of derivative has a specific meaning in math. For example, the second derivative measures the rate of change of the first derivative. Sometimes, you need to calculate the fifth order derivative also. Therefore, we introduce a fifth derivative calculator that enables you to calculate quickly.

## Formula used by 5th Derivative Calculator with steps

The derivative of a function can be calculated by a derivative using a definition calculator, which follows the limit definition of derivatives. It is simply the rate of change in the function with respect to a variable. The fifth order derivative calculator uses this formula to perform calculations.

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

For the fifth order derivative,

$f'''''(x)=\frac{d^5y}{dx^5}{2}lt;/p>

To calculate the fifth order derivative, you have to apply the derivative five times on the given function. So, it is a long and tricky process. Our derivative calculator allows you to find the fifth derivative without manual calculations.

The fifth derivative is sometimes calculated in physics, defined as the fifth derivative of the position function with respect to time. Similarly, acceleration is the second derivative of velocity with respect to time.

## Fifth derivative example

To calculate the fifth derivative of tan(3x), assume that,

$y=\tan 3x{2}lt;/p>

We need to calculate the 5th derivative of tan 3x. For this, we need to differentiate tan3x 5 times. In other words we need to calculate all first five derivatives one-by-one. Now differentiating the function with respect to x,

$\frac{dy}{dx}=\frac{d}{dx}(\tan 3x){2}lt;/p>

Since the tan 3x derivative is 3sec^2(3x), therefore,

$\frac{dy}{dx}=3\sec^2(3x){2}lt;/p>

We can write about equation as,

$y_1=3\sec^2(3x){2}lt;/p>

Now to calculate the second derivative, we need to differentiate the first derivative of tan3x. You can also use a second derivative calculator to differentiate tan3x twice.

$\frac{d^2}{dx^2}=y_2=\frac{d}{dx}(3\sec^2(3x)){2}lt;/p>

$y_2=9(2\sec 3x.\frac{d}{dx}(\sec 3x){2}lt;/p>

$y_2=18\sec 3x(3\sec 3x\tan 3x){2}lt;/p>

$y_2=54\sec^2(3x)\tan 3x{2}lt;/p>

Now to calculate the third derivative, differentiate the second derivative of tan3x.

$y_3=\frac{d}{dx}(54\sec^2(3x)\tan 3x){2}lt;/p>

Now we have a product of two functions in the above equation, therefore, by using product rule we get

$y_4=648\tan 3x\sec^2 3x(\tan^2 3x+2\sec^2 3x){2}lt;/p>

Similarly, the fifth derivative of tan(3x) is,

$1944(2\sec^6 3x+11\tan^2 3x\sec^4 3x+2\tan^4 3x\sec^2 3x){2}lt;/p>

## How to find the Fifth Derivative Calculator with steps online?

Finding the derivative calculator to compute the 5th derivative requires following some simple steps. These steps are given below.

- Open your desired browser and navigate to the search engine as google.
- On google search bar, search for the fifth derivative calculator.
- Google will provide you with a list of different websites that offer online tools. Choose our fifth derivative calculator with a graph, because it is free to use.
- After choosing our online tool, you can input any function to find derivatives.

## How does the Fifth Derivative Calculator with steps work?

Every online tool works on the provided input. Similarly, the 5th derivative calculator also works by providing an input function. It provides you the 5th derivative of a function by using the derivative formula in the backend. It provides you the 5th derivative by applying the derivative formula five times.

The fifth derivative calculator works when a user provides a function. It analyzes the function and identifies the variable by which the function is to be differentiated. It also determines that either the given function is differentiable or not and then provides you a step-by-step solution.

## Why use the 5th Derivative Calculator with a graph?

The derivative has many applications in different fields of science and real life. For example, it is used in physics to calculate the rate of change displacement with respect to time, which is the first derivative. In real life, it helps to calculate the rate of change of profit and loss at a specific point by using derivatives. Our derivative at a point calculator makes these calculations easy for you.

While doing calculations of the fifth derivative, you also have to calculate the previous four derivatives of a function one by one. But it is a lengthy and tricky process since you should know all four derivatives of the function. Therefore, it would be best for you to use this calculator online. Because our advanced calculator uses all of the differentiation rules accurately.

## Benefits of using Fifth Order Derivative Calculator with steps

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

- It is easy to use because you need to follow some simple steps.
- It provides you with the calculations of the fifth derivative with a 100% accurate solution.
- It is free of cost, so you don’t have to pay for premium tools.
- It saves you from long-term derivatives calculations so you can learn more quickly.
- You can practice with different examples again and again, like a physical calculator.

## How to use 5th Order Derivative Calculator?

Using an online derivative calculator to find the fifth derivative allows you to save the time and energy you spend on manual calculations. You can do calculations of the fifth derivative by using the following steps.

- 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 five 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, this calculator will provide you with the exact solution within a few seconds. It will also display the derivative graph so you can visually see the rate of change.

## Frequently asked questions

### What is the 5th derivative called?

The fifth derivative in physics is known as crackle when it is calculated with respect to time. It usually helps to find out the rate of change of fourth derivative of position function with respect to time.

### How do you write the fifth derivative?

The fifth derivative of a function f(x) can be written as;

$f'''''(x)=\frac{d^5y}{dx^5}{2}lt;/p>

Or, you can denote it by f5(x) to make it more readable.

### What is the easiest way to find derivatives?

The easiest way to calculate the derivative of a function is to use the differentiation laws. Or you can also use our derivative calculator that makes it simple for you.

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