# Second Derivative Calculator

## Second Derivative Calculator

Determining the rate of change of a function in terms of its variables is defined as derivatives. Second Derivative Calculator with steps is a free online tool that provides the function's second order derivative. The derivative second calculator help you evaluate second derivative quickly and accurately.

Derivatives deal with variables like x and y, functions like f(x), and the changes in the variables x and y. A function's derivative is denoted by the symbol f'(x). It signifies that the function is the y derivative with regard to x. Differentials have the symbols dy and dx. The second derivative is also known as double differentiation because it is the derivative of the derivative of a function.

## How to Use a Second Derivative Calculator?

Follow these simple steps to use the second order derivative calculator:

Step 1: In the given input field, type the function.

Step 2: Select the variable.

Step 3: To obtain the derivative, click the "calculate" button.

Step 4: Finally, the output field will show the second order derivative of a function.

Besides finding double derivative, you can also learn how to find derivative of a slope or curve while using approximate value calculator step by step.

## Formula used by 2nd derivative calculator:

The derivative formula is one of the most fundamental notions in calculus to find the second derivative. For a variable 'x' with an exponent of 'n,' the derivative formula is defined. The exponent 'n' can be a rational fraction or an integer. As a result, the derivative is calculated using the following formula:

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

## How to search for a second derivative calculator?

• Just type calculator-derivative.com in the URL bar of your browser.
• The home page of the website will be displayed; there are different derivative calculators available.
• Click on the second order derivative calculator. Enjoy calculations!

## Example:

Q: calculate second order derivative of x 1/3.

Solution:

$$\frac {d^2}{dx^2} \left( x^{(\frac{1}{3})} \right) \;=\; \left[ - \frac{2}{9x^{\frac{5}{3}}} \right]$$

Related:You can also calculate partial derivative with respect to one variable by making other variable constant in second derivative equation. For this regard use first partial derivative calculator. The user only has to enter the function, the variable to differentiate to calculate. The partial derivative will be displayed as a result automatically.

### What exactly is a second-order derivative?

The derivative of the first derivative of the given function is the second-order derivative. The graph's curvature or concavity is usually represented by the second derivative of a function. The graph of a function is upwardly concave if the second-order derivative value is positive.

### What are the benefits of an online second derivative calculator?

This higher order derivatives calculator saves your time and effort as well. You have to put just your equations and the output will be shown in seconds. It also displays all step by step calculations of a particular function.

### What is the difference between first-order differential equations and second-order differential equations?

A solution to a second-order difference equation can be found using the same method as a first-order difference problem. The only difference is that we require the values of x for two values of t, instead of just one, to start the process with a second-order equation.

### What does double derivative tell you?

The second derivative of a function measures the instantaneous rate of change of its first derivative that is already calculated. The sign of the second derivative also tells you that whether the slope of tangent line is increasing or decreasing.

For masuring that slope of tangent line, double derivative calculator is one the free and accurate resource.

### What is the second derivative test?

The second derivative test involves the calculation of derivative of a function two times. It is a way to calculate absolute maximum and minimum value of a real-valued function that is defined on a closed or bounded interval. The second derivative test calculator will tell us how the instantaneous rate of change is increaased of decreased at the boundary interval.

### What is the double differentiation of y=e3xcos2x?

Given that,

$$y=e^{3x} cos2x$$

Differentiating with respect to x and using product rule,

$$\frac{dy}{dx} \;=\; \frac{dy}{dx} (e^{3x} cos2x)$$ $$\frac{dy}{dx} \;=\; 3e^{3x} \; cos⁡2x - 2e^{3x} \; sin⁡2x$$

Again differentiating with respect to x.

$$\frac{d}{dx} \frac{dy}{dx} \;=\; \frac{d}{dx} (3e^{3x} \; cos⁡2x - 2e^{3x} \; sin⁡2x)$$ $$\frac{d^2y}{dx^2} \;=\; 9e^{3x} \; cos⁡2x - 6e^{3x} \; sin⁡2x - (6e^3x \; sin⁡2x + 12e^3x cos⁡2x)$$ $$\frac{d^2y}{dx^2} \;=\; -3 \; cos⁡2x - 12e^{3x} \; sin⁡2x$$

So in this way, you can calculate the double derivative of this type of function. Moreover, double differentiation calculator also provides this type of detailed results with all possible steps.

### How to find the second derivative of a function?

The second derivative of function may calculate manually by following below steps. However, you can also find the second derivative calculator for this purpose.

1. Find the first derivative of the given function and then simplify it if necessary.
2. Apply the derivative again on the first derivative of the function.
3. Simplify the solution to get exact value of second derivative.

Online derivative calculator gives all online tools related to derivation. Such as implicit derivative calculator and directional differentiation calculator for free.

### Alan Walker

Last Updated September 20, 2022

I am Mathematician, Tech geek and a content writer. I love solving patterns of different math queries and write in a way that anyone can understand. Math and Technology has done its part and now its the time for us to get benefits from it.