# Second Derivative Calculator

## Introduction to Second Derivative Calculator

Second Derivative Calculator with Steps is an online tool that calculates the derivative of a function up to order two. It applies the derivative formula two times on a given function.

In mathematics, online tools provide an additional way for students and mathematicians to learn faster. We introduce an online tool for this purpose that works efficiently.

## What is a Double Derivative Calculator?

2nd derivative calculator is an online free tool that makes the concept of derivatives easier. It helps you calculate the second derivative of a function step by step and computes all possible actions.

Although the derivative is not a difficult concept, sometimes it may be challenging to compute the second derivative because it is used to find the maximum and minimum values. Using the Second Derivative Calculator is helpful to compute these computations.

## How to use the Second Derivative Calculator?

The Double Derivative Calculator is an efficient and powerful tool that can be used by following elementary steps. These steps are:

1. Access the website from your browser, or you can use the Derivative Calculator with steps Math app on your android device.
2. You have to write down the function in the “Enter Function” box on the website page. Or load an example to see how to use this Calculator.
3. Choose the variable from the drop-down list of the “With Respect to” box.
4. You can review the function shown after you enter it in the box.
5. In the last step, click on the “Calculate” button.

As you click on the calculate button, the website will start processing. And the website will show the step-by-step results within a few seconds.

## Formula used by 2nd Derivative Calculator

Since the derivative of a function tells how much the function is changed with respect to the independent variable. But the second derivative means the instantaneous rate of change of a function.

The second Derivative Calculator applies the derivative formula twice on a given function. In the first step, it finds the first derivative by using the derivative formula one time. Then it applies the derivative formula again. Such as:

If y=fx is a function, applying a derivative formula on y.

$$y' \;= \; \frac{d}{dx}(y) \;=\; \frac{d}{dx}\{f(x)\}$$

Again applying the derivative on y with respect to x.

$$y'' \;=\; \frac{d}{dx}(y') \;=\; \frac{d}{dx}\Biggr[\frac{d}{dx}{f(x)}\Biggr]$$

It can be written as,

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

This formula is used by the Second Derivative Calculator with steps.

## Why to Use

The main reason for calculating the second derivative of a function is to analyze the rate of change with respect to its independent variable. The use of a second derivative calculator helps you by conducting a graph according to the difference in the function. The double Derivative Calculator discusses the instantaneous change on every point in the diagram.

In mathematics, mathematicians use the second derivative test to check the concavity of curvature of the graph of a function. The second derivative calculator with steps not only computes the second derivative it also shows the curvature by plotting the graph. That’s why there is a need to use this tool to help in the solution and every single step of its derivations.

## Benefits of using Second Derivative Calculator

The 2nd Derivative Calculator is a powerful and efficient tool with many features and applications. It is beneficial for students because it saves time and effort in doing manual calculations.

Some of the significant benefits of using this Calculator are bellowed:

1. It provides the result in a step by step manner.
2. It is easy to use because it contains simple steps.
3. Second Derivative Calculator step by step is a free online tool. You don’t require paying any fee or completing any offer to access it.
4. The website page does not show pop-up ads, making it a unique tool.
5. If you are a new user, the website provides you with a load examples option to understand how to use it.
6. There are meager chances of error in results because it computes the derivative accurately. It also verifies the results by integration.
7. The Double Derivative Calculator can handle any function like exponential, trigonometric, polynomial, etc.
8. It saves your time in doing manual calculations by providing the results within a few seconds.
9. You can also find the root of a function using the Second Derivative Calculator.

## What is the use of Second Derivative?

The second derivative is used to measure the instantaneous rate of change of a function with respect to an independent variable. It is also used to check the curvature of the graph of a function. It can tell us the maximum and minimum value of a function. The second derivative of a function also suggests that the slope of the tangent is positive or negative.

### Alan Walker

Last Updated June 02, 2022

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.