# Derivative Calculator

The derivative calculator is a free online tool that displays the derivative of the given function. BYJU’S online derivative calculator tool makes the calculations faster, and it shows the first, second, third-order derivatives of the function in a fraction of seconds.

## How to Use the Derivative Calculator?

The procedure to use the derivative calculator is as follows:

Step 1: Enter the function in the respective input field and choose the order of derivative

Step 2: Now click the button “Calculate” to get the derivative

Step 3: The derivative of the given function will be displayed in the new window

### What is the Derivative of a Function?

In calculus, one of the basic concepts is the derivative of a function. It occupies the central concept in calculus. We know that differentiation and integration are the two important concepts. Differentiation is the process of finding the derivative of a function, whereas integration is the process of finding the antiderivative of a function. The derivative of a function describes the rate of change. That means that it shows the amount by which the function is changing at the given point.

### Standard Form

The standard form to represent the derivative of a function is given below:

An infinitesimal change in the variable “x” is denoted by dx. Thus, the derivative of the variable “y” with respect to the variable “x” is given by dy/dx.

## Solved Examples on Derivatives

Example 1:

Find the first derivative of f(x) = 8x2 + 12x.

Solution:

Given function: f(x) = 8x2 + 12x.

Now, differentiating the function with respect of x, we get

(d/dx) (8x2 + 12x) = (d/dx) (8x2 ) + (d/dx)(12x)

(d/dx) (8x2 + 12x) = 16x + 12

Therefore, the first order derivative of the function 8x2 + 12x is 16x + 12.

Example 2:

Find the third derivative of f(x) = 14x4 – 2x.

Solution:

Given function: f(x) = 14x4 – 2x

Now, differentiate the function with respect to x, we get

First derivative:

(d/dx)(14x4 – 2x) = (d/dx)(14x4) – (d/dx)(2x)

(d/dx)(14x4 – 2x) = 56x3 – 2

Second derivative:

(d2/dx2)(14x4 – 2x) = 168x2 – 0

Third derivative:

(d3/dx3)(14x4 – 2x) = 336x.

Therefore, the third derivative of f(x) = 14x4 – 2x is 336x.

Example 3:

Find the fifth derivative of f(x) = 6x7 + 5x3 – 2x.

Solution:

Given function: f(x) = 6x7 + 5x3 – 2x.

To find the derivatives of the given function, differentiate the function with respect to x.

First derivative:

(d/dx)(6x7 + 5x3 – 2x) = (d/dx)(6x7) + (d/dx)(5x3) – (d/dx)(2x)

(d/dx)(6x7 + 5x3 – 2x) = 42x6 + 15x2 – 2

Second derivative:

(d2/dx2)(6x7 + 5x3 – 2x) = 252x5 + 30x – 0

Third derivative:

(d3/dx3)(6x7 + 5x3 – 2x) = 1260x4  + 30

Fourth derivative:

(d4/dx4)(6x7 + 5x3 – 2x) = 5040x3 + 0

Fifth Derivative:

(d5/dx5)(6x7 + 5x3 – 2x) = 15120x2

Hence, the fifth derivative of f(x) = 6x7 + 5x3 – 2x is 15120x2.

## Frequently Asked Questions on The derivative calculator

### What is the derivative of zero?

In calculus, differentiation is the process of finding the derivative of a function. We know that the differentiation of any constant value is zero. Thus, the derivative of 0 is 0.

### What are the different methods to find the derivatives?

The different methods to find the derivative of a function are as follows:

• Calculating the derivative by definition
• Product Rule
• Chain Rule
• Implicit Differentiation
• Quotient Rule

### Define the first and second-order derivative.

Graphically, the first-order derivative defines the slope of the given function at a point. The second-order derivative explains how the slope changes over the independent variable for the given function.