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# Fourth Derivative Calculator + Online Solver With Free Steps

The online **Fourth Derivative Calculator** is a free tool that allows you to find the fourth-order derivative of a mathematical function. The tool takes the order of derivative and function expression as its input.

The **output** calculator’s output desired order derivative of the given function. It is a powerful tool for students, mathematicians, and researchers to solve their problems quickly.

## What Is the Fourth Derivative Calculator?

**The Fourth Derivative Calculator is an online tool that calculates the fourth-order derivative of any complex function within a few seconds.**

The **function’s derivative** means how the function changes according to its dependent variable. The higher order derivatives extract more useful information about functions like extremum or concavity.

There are many applications in physics, math, and artificial intelligence where **higher-order** derivatives prove to help solve the problem. Many differential equations require fourth-order derivatives to solve them.

But if the functions are complex and involve more than one variable, it is difficult to find their derivatives. Therefore we offer you this advanced tool known as the **Fourth Derivative Calculator** to easily get solutions for your problems.

You can use this handy tool in your browser whenever you need it. It is an entirely free tool with unlimited usage capacity.

## How To Use the Fourth Derivative Calculator?

To use the **Fourth Derivative Calculator,** you need to insert the order of derivative and the mathematical expression for your function. The additional feature of this calculator is that it can calculate any order derivative of the input function.

The calculator’s interface is simple and well organized. All the input spaces have labels with them for understanding their use. The stepwise guidelines for using the calculator are given below.

### Step 1

Enter the order of the derivative in the ‘**N**’ field. For the fourth-order derivative, this ‘**n**’ should be equal to **4**.

### Step 2

Now put the expression of the function in the ‘**F(x)**’ field.

### Step 3

In the end, to get the solutions, press the ‘**Submit**’ button. It will present you with the fourth-order derivative of the given function.

## How Does the Fourth Derivative Calculator Work?

The fourth derivative calculator works by finding the **fourth-order derivative **of the given function. The value of ‘**n**’ in the calculator shows the required order of the derivative.

This value should be equal to** four **to calculate the fourth-order derivative. This calculator is useful when there is knowledge about the derivative and its importance in calculus.

### What Is the Derivative?

The derivative is the rate of change of one quantity with respect to another. The procedure of determining the derivative of a function is called **differentiation**.

The derivative of a function ‘**f(x)**’ is denoted by ‘**d/dx (f(x))**’. The meaning of the derivative in calculus can be understood by considering the curve of a function ‘**f(x)**’ and then taking two points on it. One is ‘**(x, f(x))**’ and the other is ‘**((x+h), f(x+h))**.’

Afterward, draw the** secant **line on this curve that passes through these two points. When the distance between the two points is approximately **zero**, the second point co-joins the first point,t, and eventually, the secant line becomes the **tangent **line.

The** slope** of this tangent line is considered the derivative of a function in calculus. It is defined mathematically as:

**d/dx (f(x)) = slope of the tangent = $ \lim_{h\to 0} \frac{f(x+h) – f(x)}{h} $**

The above-limit formula is used to calculate the derivative of a function, and it is called finding the derivative by using the** first principle**.

The derivatives are applied to optimize the functions. The intervals where the function is either increasing or decreasing are also found by using the derivatives. They are used to determine a quantity’s velocity by calculating the displacement derivative.

### Higher Order Derivatives

The higher order derivatives, such as the fourth derivative, are determined by finding the **successive **derivatives of a given function. For instance, when it is required to find the second order derivative, first find the first derivative and then take the derivative of the first derivate.

Similarly, the fourth-order derivative can be calculated by taking the first, second, third, and fourth derivatives one after the other. The fourth derivative is denoted by $d^4y/dx^4$.

### Primary Rules of the Derivatives

Some primary rules are used while finding the derivatives. These rules are explained below.

#### Power Rule

The power rule states that the derivative of a function with an exponent is equal to that exponent multiplied by the function with one** decreased** power.

#### Sum and Difference Rule

This rule defines the distributive property of the differentiation process. The process can be **distributed **over summation and subtraction.

#### Product Rule

When finding the derivative of a function that is the **product **of the two functions, then the product rule states the derivative of that function in the following way.

The derivative is equal to the summation of the first function multiplied by the** derivative** of the second function and the second function multiplied by the** derivative** of the first function.

#### Constant Rule

The derivative of the constant is equal to** zero** according to the constant rule of the derivative.

## Solved Examples

For a better understanding of how the calculator works, let’s have a look at some solved examples.

### Example 1

A physics student is asked to find the jounce for a given position vector in the exam. For this, he needs to calculate the fourth-order derivative of the following function.

\[ f(x) = 3x^{5} + 2x^{3} -\, 6x + 4 \]

### Solution

This problem can be easily solved using the Fourth Derivative Calculator. The answer is given as follows:

\[ \frac{d^4}{dx^4} (3x^{5} + 2x^{3} -\, 6x + 4) = 360x \]

### Example 2

While solving a vision problem, a machine learning researcher encounters a function. To further solve the problem, it is required to find out the fourth-order derivative of the function.

\[ f(x) = x^{2} sin(x) \]

### Solution

The fourth order derivative for the above function is given below:

\[ \frac{d^4}{dx^4} (x^{2} sin(x)) = (x^{2} – 12) sin(x)\, -\, 8x cos(x)\]