## Introduction to Third Derivative Calculator:

Third derivative calculator is an online tool that helps you to **find the third derivative** of the function in a few seconds. Our tool is used to evaluate the rate of change of the second derivative function f``(x).

Our 3rd derivative calculator is a beneficial tool for students, teachers, professionals, or researchers for making notes, assignments, or projects; just click on it and get solution of any third derivative problem.

## What is the Third Derivative?

The third derivative of a function is the rate of change of the **rate of change of original function** which means derivation of the second derivative f``(x). In mathematical notation, f(x) is a function, and the third derivative, f′′′(x) or dx^{3}/d^{3}f, represents the rate of change of the second derivative, f′′(x).

It is used in various fields like in physics the third derivative is known as "jerk" or "jolt" in kinematics, and in engineering. It is used in the analysis of mechanical systems like vibrations and forces. In mathematics, it is used in Taylor series expansions and the behavior of functions.

## How to Find the Third Derivative?

To **find the third derivative** of a function, the third derivative calculator follows some important rules of differentiation. Let us see an example of a third derivative for a better understanding.

**Example**:

$$ f(x) \;=\; x^4 + 3x^3 + 2x^2 + x + 5 $$

**Solution**:

**Step 1**:

The triple derivative calculator first of all identifies the function f(x) for calculations and see which differential rule is applied in the original function.

$ f(x) \;=\; x^4 + 3x^3 + 2x^2 + x + 5 $$

**Step 2**:

After identifying the type of function f(x), use the power rule formula for derivation.

$$ \frac{d}{dx}x^n \;=\; nx^{x-1} $$

**Step 3**:

To find the third derivative you need to compute the first derivative of the given function f(x).

$$ f’(x) \;=\; \frac{d}{dx}(x^4) + \frac{d}{dx}(3x^3) + \frac{d}{dx}(2x^2) + \frac{d}{dx}(x) + \frac{d}{dx}(5) $$

$$ f’(x) \;=\; 4x^3 + 9x^2 + 4x + 1 $$

**Step 4**: Again differentiate the function f`(x) with respect to x.

$$ f’’(x) \;=\; \frac{d}{dx}(4x^3) + \frac{d}{dx}(9x^2) + \frac{d}{dx}(4x) + \frac{d}{dx}(1) $$

$$ f’’(x) \;=\; 12x^2 + 18x + 4 $$

**Step 5**: For the Third Derivative of function f(x), you need to find the derivative of f``(x) again with respect to x.

$$ f’’’(x) \;=\; \frac{d}{dx}(12x^2) + \frac{d}{dx}(18x) + \frac{d}{dx}(4) $$

$$ f’’’(x) \;=\; 24x + 18 $$

Therefore the solution of the given example of third derivative is,

$$ f’’’(x) \;=\; 24x + 18 $$

## How to Use Third Derivative Calculator?

The triple derivative calculator has a simple layout that helps you to solve the given third derivative question immediately.

You just need to put the input value in this 3rd derivative calculator. Follow the given steps to get solution without any inconvenience.

**Enter the differential function**in the input fields for which you are evaluating the third derivative problem.- Choose the variable of differentiation from the given list.
- Check your given input function to get the correct solution of the third derivation question.
- Click on the Calculate button to get the result of the given third derivation function problems.
- If you want to understand the calculation process of our third order derivative calculator then use the load example option.
- Click the “Recalculate” button for the calculation of more examples of third derivate functions.

## Outcome from 3rd Derivative Calculator:

Third derivative calculator provides you with a **solution** as per your input problem when you click on the calculate button. It may contain as:

**Result Box**:

Click on the result button so you get the solution of your third derivative function question.

**Steps Box**:

When you click on the steps option, you get the result of third differential questions in steps.

## Why to Choose Triple Derivative Calculator:

The third order derivative calculator has many advantages that you get when you use it to solve third derivative problems. Our tool only takes the differential function and provides you a solution.

- It is a
**reliable tool**because it always provides you with precise solutions of third-derivative problems. - It is a speedy tool that provides solutions to the given third derivative problems in a few seconds.
- It is a learning tool that gives you conceptual clarity of third derivative function very easily through online platforms by sitting at home.
- 3rd derivative calculator is a handy tool that can solve various types of third derivation problems quickly and easily.
- It is a free tool that allows you to use it for the calculation of differentiation of functions three times without spending.
- Third derivative calculator is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of third derivation problems without any trouble.