# Second Derivative Calculator

Now calculate the second order derivative of the function with the help of second derivative calculator.

## Introduction to the Second Derivative Calculator

A second-order differentiation calculator is an online tool for finding the derivative of the functions online. This second derivative test calculator tool provides its users with free services without any subscription charges.

This tool gives you meaningful answers in no time. The double differentiation calculator is easy to use and has a user-friendly interface.

NOTE: Explore calculus complexity using our second derivative calculator. It harmoniously integrates with our range of tools, including the nth derivative calculator, derivative graph calculator and normal line calculator offering a holistic approach to mathematical analysis. Try our equation of normal line calculator which helps you to solve your problem within a second.

## What is the Double Derivative Calculator?

The second derivative calculator with steps is online to get the second-order derivative of the given function. The second-order derivative means that the function is differentiated two times instead of evaluating a single derivative.

This is called a second-order derivative. This 2nd derivative calculator is for the evaluation of such kinds of differentiation. The second-order differentiation calculator is easy to handle. The 2nd order derivative calculator gives accurate and reliable results in a fraction of a second.

The second order derivative calculator helps students, beginners, and others away from long and hectic calculations.

## Formula Used by 2nd Derivative Calculator

A double differentiation calculator is an online tool that works on the following given formula for the process of differentiation.

$$P(x) \frac{d^2y}{dx^2} + Q(x) \frac{dy}{dx} + R(x) y \;=\; 0$$

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

Example: Find second derivative for the function tan-1x, with respect to "x".

Solution : Let's take a y = tan-1x

Differentiate w.r.t "x"

$$\frac{dy}{dx} \;=\; \frac{d}{dx} tan^{-1}x$$ $$\frac{dy}{dx} \;=\; \frac{1}{1+x^2}$$

Again differentiate w.r.t "x"

$$\frac{d}{dx} \left( \frac{dy}{dx} \right) \;=\; \frac{d}{dx}\left( \frac{1}{1+x^2} \right)$$

Related: You can get Third Derivative by using our 3rd Derivative Calculator. The Third-order derivative means that the function is differentiated three times instead of evaluating a single or double derivative.

## How does Second Derivative Test Calculator Work?

The user interface of the 2nd derivative is very easy. By following the simple given steps one can get the solution to his/her problems. The double derivative calculator usually follows the following steps to calculate the second-order derivative of the given function:

• First of all, Enter the function in the required input field.
• Select the variable w.r.t to which you want to differentiate.
• Now click on the "CALCULATE" button to get the second-order derivative.

Finally, the derivative of the function's 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.

Not only second you can also find nth derivative of a function which makes your work easy for you and gives you a step by step solution. You can click here higher order derivatives calculator to get rid of paper pencil work.

## Importance of Double Differentiation Calculator

There are myriad benefits of this 2nd derivative calculator. One of the most prominent of-course is that you get all possible intermediate steps of calculation on a screen. In a blink of eye? Not a bad deal.

So following are the benefits of using this online calculator:

• The double derivative calculator has an easy user-friendly interface.
• This calculator is easier and keeps the user away from hectic manual calculations.
• It calculates second-order derivative calculations faster.
• Second derivative calculator with steps gives you accurate and authentic results.
• The results of this double differentiation calculator are reliable.
• The second derivative calculator with steps gives you step-by-step instructions to solve the derivative problems.

Second Derivative Calculator is a powerful tools for analyzing the behaviour of functions. Moreover, you can find multivariables functions by using our online multivariable derivative calculator which is freely available on our website.

## How to Find the Second Derivative Calculator?

You can find our free 2nd derivative calculator on the web via search engines like Google. All you have to do is use keywords like “Second Derivative Calculator”, “Double Derivative Calculator” or simply “find second derivative”. Pretty sure we’d be among the top results.

On the other hand, if you use our derivative calculus website regularly as a student or as a maths expert, you can simply look it up using above keywords in our search bar.

### How to Find Second Derivative

The first derivative of the function when again differentiated is called the second derivative. To determine the second derivative of a function, the 2nd derivative test calculator suggests to follow the given steps:

• Determine the first derivative of the given function
• Now take the derivative of the function’s first derivative
• You have got the second derivative

### What is the Second Derivative Test

The second derivative test is a method of finding different behaviors of the functions at the critical points to know if the function is local maximum, local minimum, or nothing else. To test the second derivative, first determine the first derivative and find the critical point of the first derivative.

Now determine the second derivative and find the critical point of the second derivative. Now see the results that you have got and know whether it’s local maximum, minimum, or not. It can also determined from the higher order derivative calculator.

### How to Find Inflection Points from Second Derivative

For determining the inflection points from the second derivative, the second derivative at a point calculator follows some steps,

• Calculate the second derivative of a given function and put it equal to zero.
• Solve x, the value of x is the potential inflection point.
• Find the sign of the second derivative on the inflection points
• Now visualize whether it moves from positive to negative, negative to positive, or has no changes.

### How would you Find the Second Derivative of e^x

To find second derivative of ex, some steps are given,

Firstly, find the first derivative as

$$\frac{d}{dx}(e^x) \;=\; e^x$$

Now find the second derivative as

$$\frac{d^2}{dx^2}(e^x) \;=\; \frac{d}{dx}(e^x) \;=\; e^x$$

So the second derivative of ex is ex

### How to Find Concavity from Second Derivative

For determining the concavity from the second derivative, there are some simple steps,

• Calculate second derivative of a given function
• Analyze the sign of the second derivative whether it's greater or less than zero. If it's greater than zero, the function is concave up.
• If the function is less than zero, then it would be concave down but if it’s equal then the second derivative does not exist.
• Determine the inflection point and analyze if the function is concave up, concave down, or not.