The derivative calculator is an online tool that gives the derivative of the function. Kiodigital online derivative calculator tool carries out the computations quicker, and it offers the first, second, third-order derivatives of the operation soon.
Steps to use the Derivative Calculator
The method to use the derivative calculator is:
Step 1: Enter the function
Step 2: Now click the button “Calculate”
Step 3: The derivative will be displayed
Derivative of a Function
The derivative of a function is the basic concepts in calculus . It establishes the significant concept in calculus. Differentiation and integration are the two prominent concepts. Differentiation is finding the derivative of a function, whereas integration is finding the antiderivative of a function. The rate of change is described by the derivative of a function. In simpler words, it gives the amount by which the function is varying at the point.
Standard Form
The standard form to represent the derivative of a function is:
dy/dx
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.
Similarly, the second order derivative of a function is represented by d2y/dx2, third order derivative of a function is denoted by d3y/dx3, and so on.
Solved Examples on Derivative Calculator
Example 1:
Find the first order derivative of a function, y = 3×2 – 5.
Solution:
Given function: y = 3×2 – 5
Differentiating the given function with respect to x, we get
dy/dx = (2)3x – 0
dy/dx = 6x.
Hence, the first order derivative of the function y = 3×2 – 5 is 6x.
Example 2:
Determine the second order derivative of sin x.
Solution:
Given function, y = sin x.
As we know, the differentiation of sin x is cos x.
I.e., (dy/dx)(sin x) = cos x.
To get the second order derivative, again differentiate the above function.
I.e., Second order derivative, (d2y/dx2)sin x = – sin x.
Therefore, the second order derivative of sin x is – sin x.
Example 3:
Find the second order derivative of 4×4 – 3x.
Solution:
Given function, y = 4×4 – 3x.
Finding First Order Derivative:
First, differentiate the given function with respect to x.
I.e., dy/dx = 16×3 – 3.
Finding Second Order Derivative:
To find the second order derivative, again differentiate the function.
I.e., d2y/dx2 = 48×2 – 0
Hence, we get,
d2y/dx2 = 48×2.
Therefore, the second order derivative of 4×4 – 3x is 48×2.
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Frequently Asked Questions on Derivative Calculator
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.
What are the different types of methods to find the derivatives?
- Calculating the derivative by definition
- Product Rule
- Chain Rule
- Implicit Differentiation
- Quotient Rule
What is 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.
