Introduction to Product Rule Calculator

Product Rule Calculator with steps is an online tool to calculate the derivative of a function by using the product rule. It applies the derivation formula to the function consisting of two or three functions by following the product rule for the derivative.

When doing manual calculations using the product rule of derivative, you may forget to apply the derivative formula on any term because of a lack of practice. Here we introduce online software that can help you in computing derivatives for more than one function.

What is the Derivative Product Rule Calculator?

Product Rule Calculator with steps is online free software that is helpful to calculate the derivative of a combination of two functions. In other words, this Calculator helps you to differentiate two or more functions that are multiplied together.

All derivative rules play an essential role in calculus, including the product rule. So, if you want to learn the concept of derivatives, you have to understand all the rules. Product Rule Derivative Calculator makes understanding this concept easier by providing step-by-step solutions.

You can also consult other tools on this website, like Quotient Rule Calculator and Chain Rule Calculator.

How to use a product rule of differentiation calculator?

There are elementary and easy steps to using this tool.. These are as follows:

  1. First, you need to enter the function in the “Enter Function” box. Or you can go with the already given example to check how to use this Calculator.
  2. You need to choose the variable from the list given below in the “With Respect To” box.
  3. Now in the last step, press the “Calculate” button.

After clicking on the calculate button, the tool will start computing the derivative, and it will show the result after a few seconds.

Formula used by Product Derivative Rule Calculator

Since the term derivative tells us the rate of change of a function, the product rule is a rule for derivative, which is applied if a function is a combination of two functions.

The Product Rule Calculator uses the following formula for finding derivatives of two functions multiplied together.

$$ \frac{d}{dx}(uv) \;=\; v. \frac{du}{dx} \;+\; u. \frac{dv}{dx} $$

Where u and v are two functions depending on x.

This Calculator can also handle three functions combined together. Formula to three functions is:

$$ \frac{d(uvw)}{dx} \;=\; uw \frac{dv}{dx} \;+\; vw \frac{du}{dx} \;+\; uv \frac{dw}{dx} $$

Where u, v and w are three functions depend on the independent variable x.

Example:

Find the derivative of y = xsinx.

Since the function y contains two functions x and sinx. We will use the product rule of derivative to solve this example.

Step I:

Applying derivatives on both sides of the given equation.

$$ \frac{dy}{dx} \;=\; \frac{d}{dx}(xsinx) $$

Using product rule,

$$ \frac{dy}{dx} \;=\; sinx \frac{d}{dx}(x) \;+\; x \frac{d}{dx}(sinx) $$

Now,

$$ \frac{dy}{dx} \;=\; sinx \;+\; xcosx $$

This example is solved by using product rule because the function y is a combination of two functions.

Why to use a Product Rule Calculator with steps?

The concept of the derivative is essential in calculus because it can solve our daily life problems like it can tell the maximum and minimum value, rate of change in speed of a machine, etc. There are different tools available on the website that make it easy to solve these problems regarding derivatives.

The Product Rule of Differentiation Calculator is one of these tools available online. It helps you practice by showing step-by-step differentiation and plots a graph for visible purpose. That’s why you need to use it for differentiation.

Benefits of using Product Rule Derivative Calculator

Using an online tool for differentiation in mathematics is always a very effective and intelligent way because it can instantly evaluate the derivative of two or more functions.

There are some significant benefits of using this tool.

  1. It saves your time which is more effective than manual calculations.
  2. It provides step-by-step differentiation accurately because there is no chance of error in the solution using the Derivative Product Rule Calculator.
  3. It verifies the solution by integrating it and showing its alternative forms.
  4. It also shows a graphical representation of the function according to the rate of change.
  5. This calculator is an efficient tool that helps students product rule calculator practice with more examples.
  6. It is free online software, so you don’t need to pay any fee.
  7. The Product Rule of Differentiation Calculator is easy to use. You need to follow some steps.
  8. It has a unique and straightforward display, making it different from other online sources.
  9. It is a potent tool having many features. Because you can find numerical roots, real and imaginary parts of the solution, domain, and range, expand the form of the solution and infinite integrals using this single tool.
  10. You don’t need to complete any offer to use the Derivative Product Rule Calculator.

FAQ’s

Why is the product rule important?

The product rule is used in calculus to help you calculate the derivative of products of functions without using the definition of the derivative. It can also be generalized to the product of three functions.

Alan Walker

Shaun Murphy

Last Updated March 28, 2022

A professional content writer who likes to write on science, technology and education.