# Third Derivative Calculator

Third Derivative Calculator

## Introduction to the Triple Derivative Calculator

A third-order derivative is an online tool for calculating the derivatives whose derivatives are of third-order. The 3rd derivative calculator gives accurate solutions to the problems.

The triple derivative calculator is free of cost as other calculators i.e derivative at a point calculator or Partial calculator which are available without any subscription charges before and after its use. This calculator saves precious time for the user by giving them quick and accurate results.

Here you can try our multivariable derivative calculator to find your solution step by step in a simple way without doing long procedure.

## What is the Third derivative calculator?

Derivatives are the rate of change of the condition according to its respective functions. The triple derivative calculator is also called a higher derivative calculator i.e second derivative, third derivative, fourth derivative and upto nth derivative.

One may also get individual higher derivative calculator for solving special problems.

This triple derivative calculator with steps calculates the third-order derivatives with step-by-step guidance to the user. To find a function's third derivative, start by finding its second derivative. After that, use the sum rule, product rule, quotient rule, and chain rule on the second derivative. This way, you can calculate the third derivative step by step. It helps to differentiate thrice all other complex functions of mathematics.

Note: Click here to make your work easy by using our free calculator quotient of two functions calculator.

## Formula Used by Third order Derivative Calculator

The triple derivative calculator is based on the method of differentiation. The third derivative formula says that it is the rate of change at which the second-order derivative changes.

The formula used to analyze this type of rate of change is as follow:

$$\frac{d}{dx} \left( \frac{d^2y}{dx^2} \right) \;=\; \frac{d^3y}{dx^3} \;=\; f'''(x)$$

Let's see how to use this formula for the calculation of third derivative of a function.

Example: Find the third derivative for the function cos(2x), with respect to "x".

Solution: Let's take a y = cos(2x)

$$y \;=\; cos(2x)$$

Differentiate the function w.r.t "x"

$$\frac{dy}{dx} \;=\; -sin(2x) \frac{d}{dx}(2x) \;=\; -2sin(x)$$

Again differentiate w.r.t "x" to get the second order derivative

$$\frac{d^2y}{dx^2} \;=\; -2.cos(2x) \frac{d}{dx}(2x) \;=\; -4cos(2x)$$

Note: You can also find the second derivative using our 2nd order differentiation calculator.

For finding the 3rd order derivative, again differentiate it w.r.t "x".

$$\frac{d^3y}{dx^3} \;=\; -4 (-sin(2x)) \frac{d}{dx}(2x) \;=\; 8 cos(2x) \cdot 2$$ $$\frac{d^3y}{dx^3} \;=\; 16cos(2x)$$

## How does 3rd Derivative Calculator Work?

The third derivative calculator with steps works on the process of differentiation. This higher derivative calculator follows the basic rules of differentiation to calculate the third-order derivative for that particular function.

The user interface of the higher derivative calculator is very easy and simple. By following the simple given steps one can get the solution of the given function.

The higher derivative calculator usually follows the following steps to calculate the third-order derivative of the given function:

• Open the calculator from our web portal.
• Put the function in the required input field.
• Or you can load the example from the drop-down list.
• Select the variable w.r.t to which you want to differentiate.
• Now click on the "CALCULATE" button to get the third-order derivative.

Finally, the rate of change of the second derivative will display on the screen. Not it only contain the double derivative, but also it has possible intermediate steps, plots and trigonometric form of given function.

So click on re-calculate button for the solution of another problem.

## How to Find the Third Derivative Calculator with steps?

It is quite easy task to find an online triple derivative calculator. You can search them by different approaches.

1. Enter the exact URL of the calculator i.e. https://derivative-calculators.com/third-derivative-calculator.
2. Type the keywords as "third derivative calculator","3rd derivative calculator" or "find the triple derivative". Hopefully we will available in top results of search engine.

## Benefits Using Third order Derivative Calculator

A 3rd derivative calculator is an online tool that is very essential in mathematics. It is an important tool that is also used in physics as well as in mathematics. This higher derivative calculator calculates the derivatives using differentiation techniques.

• The third derivative calculator with steps gives the solution with step-by-step instructions.
• The results of the triple derivative calculator are authentic and reliable.
• This calculator gives you results in fractions of seconds and save your time from manual calculations.
• The third order derivative calculator gives three derivatives and gives answers with step-by-step instructions.
• This 3rd derivative calculator is a freely available tool without any subscription.
• By typing the simple keyword from your keyboard one can get this tool on his/her device(hopefully in few of top results).

Hope so you may like our efforts made on this tool. Also try our other derivative relevant tools for reliable learning.

## Frequently Asked Question

### What is Third Derivative Test

The third derivative test is a method to test the behavior of a function on its critical point to understand if it corresponds to local minimum, local maximum, or none of them. To do the third derivative test,

• Find third derivative of function
• Determine the third derivative at its critical point
• Now analyze if the function has a local minimum, local maximum, or not.

### What does the Third Derivative Tell You

The third derivative tells the curvature of the changing function. However, it also tells about the inflection points which helps to identify the curvature of the changing functions. A question arises of how to find third derivative sign and what it represents.

When the third derivative changes sign and if it is not zero then it means it has an inflection point means third derivative represents it.

The third derivative tells about the rate of change of the curvature which indicates whether the curvature is increasing or decreasing. On the other hand, it also describes the higher-order behavior beyond the first and second derivatives.

### Is the Third Derivative Positive or Negative?

If the third derivative positive or negative depends on the behavior of curvature. If the triple differentiation is positive, then the curvature is increasing at a point on the function means the function is becoming more curved upwards.

If the third derivative is negative then the curvature is decreasing at a point on the function means that the function is becoming less curved upward. Moreover, the sign of the third derivative describes whether the function is increasing or decreasing at a given point.

### What is Third Derivative Test Point of Inflection

The third derivative has a point of inflection test on a curve. For that, first, determine the derivative of 3rdof the given function.

Now identify the points where the third derivative is zero and analyze the behavior of the function.

Then do the second derivative test on the given point.