# Product Rule Calculator

product-rule-calculator

## Introduction to the Product Rule Derivative Calculator

The product rule differentiation calculator is an online tool that is a freely available website that makes calculations to find the derivative functions. The product rule solver for sure finds the derivatives that are comprised of some small differential functions.

This product rule calculator gives the solution in no time. This product rule calculator with steps is free of cost without paying any subscription charges.

This calculator saves precious time while doing manual calculations. The Derivative using Product Rule Calculator has a user-friendly interface. The results should be error-free with a step-by-step illustration.

Note: There is a relationship between product rule and chain rule which lies in their application. When you have a function that involves both multiplication (product rule) and composition (chain rule), you may need to use both rules together to find its derivative. click here composite function calculator to unlock the ability to find derivatives of complex composite functions.

## What is a Product Rule Differentiation Calculator?

A product rule calculator with steps is the best online tool that holds the product rule formula for finding the derivatives of the small differential functions.

The product rule is that in which the multiplication of two smaller derivative functions has been done. This product rule solver makes it easier for the user to find the product of two differential functions.

When there is a condition when one derivative function is the product of another derivative function, then we used this product rule solver to find the derivatives of such differential functions.

On the other hand, if the function is in the form of P(x)/Q(x), then we also offers derivative quotient rule calculator to solve it with steps.

## Formula Used By Product Rule Calculator with Steps

The formula that is used by this product rule derivative calculator is based on the product rule. The product rule is stated as:

“The derivative of the new function equals the derivative of the first function times the second function + the derivative of the second function times the first function”

Mathematically,

$$\frac{d}{dx} \;=\; f(x)g'(x) + f'(x)g(x)$$

Let's see how this formula helps to calculate derivatives in the below example:

Example: Differentiate the function y = x4(x3+2x2+5)

Solution: We have a function:

$$y \;=\; x^4(x^3+2x^2+5)$$

Differentiate the function w.r.t "x" by using the above mentioned formula.

$$\frac{dy}{dx} \;=\; x^4 \frac{d}{dx}(x^3+2x^2+5) \;+\; (x^3+2x^2+5) \frac{d}{dx} x^4$$ $$\frac{dy}{dx} \;=\; x^4 (3x^2+4x) \;+\; (x^3+2x^2+5)(4x^3)$$ $$\frac{dy}{dx} \;=\; 3x^6 + 4x^5 + 4x^6 + 8x^5 + 20x^3$$ $$\frac{dy}{dx} \;=\; 7x^6 + 12x^5 + 20x^3$$

And thats it is...

In the same way our calculator will provide you steps in details.

Note: Also try our derivative calculator second to take the derivative of the derivative.

## How does the Product Rule Calculator Work?

Following steps are usually performed to calculate the smaller differential functions in the derivative using product rule calculator:

1. Enter the function in the form of f(x).g(x).
2. Or can load the example from the drop-down list.
3. Select the variable w.r.t to which you want to differentiate the function.
4. Now, just press the "CALCULATE" button the step by step detailed result for dy/dx will appear on the screen.

## How to Find the Product Calculator?

It is not difficult to find a product rule calculator. There are two possible ways to find this calculator. These are:

• First of all, if you are a regular user of this website you can directly search the URL of this calculator. Also you can bookmark this derivative online tools website for instant using.
• On the other hand, you can search the calculator by its name as "product rule calculator" or "product rule solver".

You can either select any of these two methods to find this tool on internet.

## Reasons to Choose Product Rule Differentiation Calculator

Following is the list of benefits while using this product rule calculator with the steps listed below:

• The product rule calculator allow us to take the derivative that we cannot multiply easily or quickly.
• The product rule solver is a totally free and easily available tool for students, scientists, and engineers.
• This tool gives error-free results with all possible steps and their calculation details i.e. instructions and graphs etc.
• The user interface of this online tool is very friendly and quite easy-to-understand.
• This product rule derivative calculator gives you results in a fractions of a second.
• This online tool is reliable, accurate & 100% error-free for it's users.
• This calculator has free unlimited access that is the user can do calculations multiple times.

No doubt product rule calculator is a great tool for helping students for mastering the calculus assignment. you can tackle even more derivatives by using derivative grapher and linearization calculator that make calculation easy and time saving for all.

### What is the Product Rule

The product rule is a method in calculus that is used to determine the derivative of the product of two functions. The product rule is helpful when dealing with the functions that are the product of two or more terms.

It helps you to differentiate functions easily without expanding them into individual terms. The differentiate the function calculator differentiates such questions easily.

### What is the Product Rule for Exponents

The product rule for exponents is a special case that occurs in product rule. The product rule for exponents applies on the functions with exponents. The derivative calculator product rule find the product rule for exponents easily. It is helpful to determine the product of two functions where one function or both functions are exponential function. here‘s the equation:

$$(u . v)’ \;=\; u’v + uv’$$

### What is the Product Rule for Logarithms

The product rule for differentiation is helpful in differentiating the product of two functions when one function or both functions involves the logarithms. The product rule calculus calculator finds it and gives a function. If one function or both functions involve logarithms then the product rule can be directly applied.

So, if both functions involve logarithms then each logarithmic term would be differentiated by using the logarithmic differentiation rule and then the standard product rule is applied on it.

### Use the Product Rule to Find the Derivative

To find the derivative using product rule, following formula is used:

$$(f.g)’ \;=\; f’.g + f.g’$$

By using this rule, the derivative would be find out.