Product Rule Calculator

The product rule functions has always been tricky for everyone but now our product rule calculator will make it easy by its automatic calculations.


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Introduction to Product Rule Calculator with Steps

A product rule solver is a mathematics tool that is used to solve derivatives of product rule functions. You can evaluate derivatives of products of two or more than two functions using this product rule calculus calculator with steps in a fraction of a second.

Whether you're a student learning calculus or a professional dealing with mathematical functions, the Product Rule Calculator is a valuable tool for computing derivatives of product functions with ease and precision.

product rule calculator

Our calculator automates the process of finding derivatives of functions that are the product of two other functions Additionally, if you would like to to calculate the derivative of a composition of functions, you can utilize our chain rule calculator.

Our calculator serves as a valuable tool for students, professionals, and anyone working with functions in calculus, helping them understand and compute derivatives efficiently and accurately.

What is the Product Rule Derivative?

The product rule is a method used to find the derivative of any function that is given in the form of the multiplication of two or more than two differentiable functions.

The Product Rule states that to differentiate the product of two functions, you take the derivative of the first function multiplied by the second function, and then add the product of the first function and the derivative of the second function.

The Product Rule is essential in calculus for finding derivatives of functions that involve the multiplication of two or more terms, and it is often used alongside other differentiation rules such as the Chain Rule and Quotient Rule.

For further exploration and to solve derivative problems involving quotient functions, you can use our quotient rule calculator. Our clauclator also evaluate complex ratio problems using the quotient rule for derivation in the run of time.

Formula behind Product Rule Derivative Calculator

The formula behind our derivative calculator product rule is,

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

f(x) is the first derivative function.

g(x) is the second derivative function

f`(x)g(x)+g`(x)f(x) is the sum result of product rule differentiation.

Evaluation Process of Product Rule Solver

The product rule calculator with steps allows you to evaluate product rule problems because It has all derivative rules built-in in its software.

When you put your derivative function in the product rule calculus calculator it will analyze the function f`g and apply the product rule for derivation. After that, it derivative first functions f according to the independent variable by keeping the other value g constant. The same procedure is done when g is differentiation and f behaves as constant. In last, you add both derivation processes like f`g + g`f.

Our product rule solver can solve the product rule derivative of multiple functions. In calculus, when dealing with indeterminate forms, especially in limits, L'Hopital's Rule becomes a valuable tool for finding limits involving functions that approach zero over zero or infinity over infinity. The l'hopital's rule calculator provides a convenient way to compute such limits without manual calculation, streamlining the evaluation process.

Let us know how the product rule derivative calculator solves problems of the derivative of the product rule with the help of an example.

Example of Product Rule Problem

Although the product rule calculator is here to help you with complex problems manual calculation is also essential to understand each step. So here we give step-by-step calculations for solving such problems,


$$ x^2 e^x $$


Differentiate using the product rule,

$$ g(x) \;=\; e^x $$

$$ x^2 \frac{d}{dx} [e^x] + e^x \frac{d}{dx} [x^2] $$

Differentiate using the exponential rule,

$$ x^2 e^x + e^x \frac{d}{dx} [x^2] $$

Differentiate using the power rule,

$$ x^2 e^x + e^x (2x) $$


$$ x^2 e^x + 2xe^x $$

Thus it is the final solution of our function with specific limits. Additionally, When it comes to solving ordinary differential equations numerically, Euler's Method is a fundamental tool used to approximate the solutions. The euler method calculator provides a simple yet effective way to compute numerical solutions to initial value problems without the need for extensive manual calculations.

Answer Comes from the Product Rule Calculator

A user gets the result of the product rule differential problem instantly after adding the input in this calculator.

  • Result section gives you a solution of the product rule from the product rule calculus calculator.
  • Possible step section provides you with a step-by-step solution of the product rule function.
  • Plot section will make a graph of the given result.
  • Recalculate button gives you a new page for more calculations.

Related: In numerical analysis, newton raphson method calculator is a powerful iterative technique used to find successively better approximations to the roots of a real-valued function. This calculator also offers a convenient way to apply this method and obtain accurate solutions to equations without manual iteration.

How to Use the Derivative Calculator Product Rule?

In our product rule derivative calculator, you can solve one or more than two product function differentiation.

The steps that should be followed while using the product rule solver are as follows:

  • Enter your desired product or function at the input box
  • Click the button “Calculate” to get the derivative
  • Solution gets after evaluation on the next page

Why Should you Use the Product Rule Calculus Calculator?

The product rule calculator with steps is a beneficial tool for you to use the product rule derivative problem easily. If you know the concept of product rules, you can deal with all types of product rule functions. On the other hand, if you do not know about this concept then you need some external help like our derivative calculator product rule to determine these problems. It provides graphs for a better understanding.

Additionally, When it comes to solving differential equations numerically, you can use our improved euler's method calculator. The Improved Euler Method, also known as Heun's Method, is a numerical procedure for approximating the solution of ordinary differential equations.

Advantages of Using Our Calculator:

The product rule derivative calculator provides a simple method when a user uses it. It gives numerous benefits while using it for evaluation.

  • It provides accurate solutions while differentiating any product function
  • The user-friendly interface of our calculator allows anyone to access it easily.
  • This calculator offers differentiating into step-by-step solutions
  • It saves time and reduces the risk of manual calculation errors.
  • It uses a calculator for a lot of different examples to calculate for clarity.

Additionally, if you're interested in exploring other mathematical calculators, you can utilize our bisect calculator. Our calculator assists in finding roots of equations using the bisection method, providing another valuable tool for numerical analysis.

Overall, the Product Rule Derivative Calculator offers numerous benefits, making it an invaluable resource for students, professionals, and anyone working with calculus in their studies or professions.

Blunders Expected while Using the Product Rule Calculator:

Users should check these errors which are mentioned below in the product rule derivative calculator to get the precise result.

  • Your expression of the function you would like to differentiate should be placed according to mathematical syntax.
  • Make sure you specify the function variable for differentiation.

Related:For further exploration and access to a wide range of mathematical calculators, you can visit our All Calculators page.

Frequently Asked Question

What is the Product Rule

The product rule is used to calculate the derivative of the product of two functions. When there is two differentiable functions then the product rule will be,

$$ (u(x)v(x))’ \;=\; u’(x)v(x) + u(x)v’(x) $$

According to the formula used by the derivative product rule calculator, to differentiate the product of two functions, the derivative of the first function should be multiplied by the second derivative and then the product of first function and the derivative of the second function is added.

What is the Product Rule for Exponents

The product rule for exponents helps to simplify the expressions involving exponents with the same base. According to this rule, when two expressions having the same base are multiplied then the exponents are added while the base is unchanged,

$$ a^m . a^n \;=\; a^{m+n} $$

In this formula used by the product rule differentiation calculator, a is any real number, and m and n on a are positive integers.

What is the Product Rule for Logarithms

The product rule for logarithms is about dealing with logarithmic expressions which states that the logarithmic product is the sum of the logarithms of the individual factors. The differentiation product rule calculator uses this statement in the form of the following formula,

$$ log_b (xy) \;=\; log_b (x) + log_b(y) $$

In this formula, b is the base of the logarithm, and x and y are the factors. This rule allows to break down the logarithm of the product into simpler parts which makes it easy to solve the logarithmic equations or simplifying the equations.

Use the Product Rule to Find the Derivative

The product rule is a derivative rule which is used to calculate the derivative of the product of two functions which is mathematically represented as,

$$ \biggr(f(x) g(x) \biggr) \;=\; f’(x) g(x) + f(x) g’(x) $$