Derivative Calculator: 1st & 2nd Derivative Calculator with Steps

Derivative Calculator is an online tool designed to calculate the derivatives of functions. It helps you to check your solutions to calculus exercises. In addition, the online calculator also assists you in practising by displaying the entire task. The derivative calculator also helps to calculate first, second, and third-order derivatives and different functions with multiple variables (partial derivatives), implicit differentiation, and computing roots of zeros. By providing interactive graphs or plots it helps visualize and understand the functions effectively. In this article, we have provided all the necessary information on how to use the derivative calculator and its functions. Read on to find out more.

What is Derivative Calculator?

A derivative Calculator is an online tool that helps to compute the value of the derivatives. It allows you to calculate the value of the derivatives in a few seconds. The result displays a minor difference in a function for one of its variables. Usually, this calculator makes the calculations faster, and it shows up to first, second, third-order derivatives of the output.

How to Use Derivative Calculator?

You can follow the steps given below to find the value of the derivatives by using an online calculator:

Step 1: Enter the function with respect to x in the input boxes available.
Step 2: Then, click on the “Calculate” button to find the value of the derivatives.
Step 3: The result will be displayed on a new window
Step 4: Click on the reset button to clear the fields and enter the various functions.

Note: We are working with our team to add a derivative calculator on this page, the steps mentioned above comply with any online calculator. Once it’s embedded on this page, you can quickly calculate and find the results within a fraction of seconds.

How Does Derivative Calculator Actually Work?

The following section explains how the calculator works manually for people with a technological background:

First, a parser (Parser is a compiler used to break the data into more minor elements from the lexical analysis phase) examines the mathematical function. Then, it converts it into a better understandable form by a computer, namely a tree. While doing this, it has to respect the order of operations. A specialty in arithmetical expressions is that the multiplication sign can be omitted sometimes; for instance, we write “5x” instead of “5*x”. The Calculator has to identify these cases and embed the multiplication sign.

The parser is written in JavaScript, based on the Shunting-yard algorithm. Thus, it can run directly in the browser. By translating the tree into Latex code, it enables immediate feedback while typing. MathJax ( a software) takes care of displaying it in the browser.

Additionally, on clicking the submit button, the calculator sends the mathematical functions and the settings (differentiation variable and order) to the server, where it is examined again. This time, the function gets transformed into a form that can be understood by the CAS or computer algebra system.

Lastly, enter the function you want to differentiate into the Derivative Calculator. Skip the “f(x) =” part as the calculator will show you a graphical version of your input while you type. Make sure that it shows precisely what you want. Use parentheses, if necessary, e. g.,

$\frac{a}{b + c}$

Thus, you can see which functions are supported by the online calculator and how to use them.

When you enter your function, click submit button, and the calculator will show the result below.

In the “Options” tab, you also have an alternative to set the differentiation variable and the order (first, second, the third derivative). You can also decide whether to show the steps and enable expression simplification.

Also, Check:

Ratio Calculator	EMI Calculator
Simple Interest Calculator	Compound Interest Calculator (Coming Soon)

Advantages Of Derivative Calculator

Using the calculator effectively is an important skill. This skill is best learned by using a calculator regularly and meaningfully.

Students who learn math by using the calculator perform better in their answers, especially in derivative calculations.
It allows people to spend more time in solving problems than a lack of time on computing.
It uses well-known rules like the product rule, the linearity of the derivative, power rule, chain rule, etc.
Applies lesser-known rules to compute the derivative of a broad array of special functions.
For higher-order derivatives, certain rules, like the general Leibniz product rule, can speed up calculations with the help of such calculators.
One can solve very tedious and most difficult arithmetic problems.
The biggest advantage is calculation is always correct.

Common Functions and Rules to Find Derivatives

Below is a list of essential rules to help you calculate the derivatives of various functions:

Common Functions	Function	Derivative
Constant	c	0
Line	x	1
	ax	a
Square	x²	2x
Square Root	√x	(½)x^-½
Exponential	e^x	e^x
	a^x	ln(a) a^x
Logarithms	ln(x)	1/x
	log_a(x)	1 / (x ln(a))
Trigonometry (x is in radians)	sin(x)	cos(x)
	cos(x)	−sin(x)
	tan(x)	sec²(x)
Inverse Trigonometry	sin^-1(x)	1/√(1−x²)
	cos^-1(x)	−1/√(1−x²)
	tan^-1(x)	1/(1+x²)

Rules	Function	Derivative
Multiplication by constant	cf	cf’
Power Rule	xⁿ	nxⁿ⁻¹
Sum Rule	f + g	f’ + g’
Difference Rule	f – g	f’ − g’
Product Rule	fg	f g’ + f’ g
Quotient Rule	f/g	f’ g − g’ f/g²
Reciprocal Rule	1/f	−f’/f²
Chain Rule	f º g	(f’ º g) × g’
Chain Rule (using ’)	f(g(x))	f’(g(x))g’(x)
$C h a i n R u l e (u \sin g \frac{d}{d x})$	$\frac{d y}{d x} = \frac{d y}{d u} \frac{d u}{d x}$

Solved Examples

Find the derivative value of $5 x 3 + 2 x 2 ?$

Solution $= d / dx (5 x 3 + 2 x 2) = d / dx (5 x 3) + d / dx (2 x 2)$
$Using multiplication by constant and power rule, = (5 \times 3 x 3 - 1) + (2 \times 2 x 2 - 1) = 15 x 2 + 4 x$
$Th us, the derivative value of 5 x 3 + 2 x 2 is 15 x 2 + 4 x$

Frequently Asked Questions (FAQs)

We have listed some frequently asked questions on the derivative calculator below:

Q1. What is the first derivative formula?
A. The first derivative is a formula for the instantaneous rate of change of one variable concerning another.

Q2. What does H mean in the derivative formula?
A. The value of

f (a + h) - f (a)

his the slope of the line through the points so

(a, f (a)) a n d (a + h, f (a + h))

, H is the so called secant line.

Q3. Can calculators solve derivatives?
A. Yes, the value x of the derivative reflects on the screen. The derivative is displayed at the bottom of the screen by the calculator.

Q4. Where can I find a derivative calculator?
A. You can find several such calculators online. We will add a derivative calculator soon on this page.

Q5. Where canI find steps to use a derivative calculator?
A. The steps to use any online claculator is given in the above article.

We hope this article on the derivative calculator was helpful. Understanding the use of a calculator will help you solve statistical problems and real-life challenges in a fraction of seconds.

If you have any queries about this article, do let us know about it in the comment section below. We will get back to you at the earliest.