Calculadora da Regra do Produto
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(f·g)' = f'·g + f·g'
About this calculator
The Product Rule Calculator automatically solves the derivative of the product of two functions. The product rule states that the derivative of f(x) times g(x) is f'(x) times g(x) plus f(x) times g'(x). Simply enter the functions f(x) and g(x) in the provided fields, and the tool calculates the derivative step by step.
This calculator is useful for calculus students who need to check exercises or understand the application of the product rule. It also serves professionals working with mathematical functions in engineering, physics, or economics. The calculation is automated, avoiding manual errors.
To use it, type two functions in the format accepted by the calculator, such as polynomials, exponentials, or trigonometric functions. The tool differentiates each function separately and applies the formula f'·g + f·g'. The result is displayed simplified when possible.
Caution: the product rule only applies when two functions are multiplied. Do not confuse it with the chain rule (composite function) or the quotient rule (division). Ensure the expression is correctly entered, especially with parentheses for complex functions.
Frequently asked questions
What is the product rule?
The product rule is a formula for differentiating the product of two functions: (f·g)' = f'·g + f·g'.
What types of functions can I input?
You can input polynomial, exponential, trigonometric, logarithmic functions and their combinations, as long as they are written in standard mathematical format.
Does the calculator show step-by-step?
Yes, the calculator displays the derivative of each function separately and then applies the product rule, showing the final simplified result.
Can I use the calculator for functions with more than one variable?
No, this calculator is designed only for single-variable functions. For multiple variables, partial derivatives are needed.
What if the function is not recognized?
Check if the function is written correctly, using operators like * for multiplication and ^ for exponents. Refer to the accepted format on the page.