Product Rule Calculator
Verified Calculation Engine
The online Product Rule Calculator helps you calculate instantly and solve problems related to Differentiation. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Applies product rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x).
d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Product rule: derivative of first times second plus first times derivative of second
Product rule for differentiating product of two functions
Inputs
Results
Worked Examples
Example 1: Basic
Find derivative of x² · sin(x)
- function1: x^2
- function2: sin(x)
- derivative: 2x·sin(x) + x²·cos(x)
- steps: f'(x) = 2x, g'(x) = cos(x), so (x²·sin(x))' = 2x·sin(x) + x²·cos(x)
Example 2: Board Level
Find derivative of (x+1)(x²+2)
- function1: x+1
- function2: x^2+2
- derivative: 1·(x²+2) + (x+1)·2x = 3x² + 2x + 2
- steps: f'(x) = 1, g'(x) = 2x
About this calculator
Overview
Product Rule Calculator evaluates Product Rule for the math / differentiation library. Primary input cue: First Function f(x) [required]: First function. Method anchor: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Product rule: derivative of first times second plus first times derivative of second. Product rule for differentiating pr.
When to use
Use Product Rule Calculator when you already know the inputs and need product rule without setting up a spreadsheet.
Inputs explained
- First Function f(x) [required]: First function
- Second Function g(x) [required]: Second function
Formula / method
d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Product rule: derivative of first times second plus first times derivative of second. Product rule for differentiating product of two functions (calculator id: product-rule-calculator).
Worked example
Worked values: function1 = x^2, function2 = sin(x) → derivative = 2x·sin(x) + x²·cos(x), steps = f'(x) = 2x, g'(x) = cos(x), so (x²·sin(x))' = 2x·sin(x) + x²·cos(x)
Interpreting results
Read the primary output as product rule under the method on this page.
Assumptions
- Product Rule is computed only from the fields you enter on this calculator. [product-rule-calculator]
- The wired execution function for `product-rule-calculator` is the source of numerical behavior.
- Real-number arithmetic is used unless product rule explicitly needs integers.
Limitations
- Edge cases outside the intended domain of product rule may error or look unstable—treat them as out of scope.
- If multiple conventions exist for product rule, this calculator uses the convention implemented in its engine path.
- Complex/branch cuts and undefined points are not always interactively annotated for product rule.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Product rule: derivative of first times second plus first times derivative of second. Product rule for differentiating product of two functions (calculator id: product-rule-calculator).
Example Calculation
Worked values: function1 = x^2, function2 = sin(x) → derivative = 2x·sin(x) + x²·cos(x), steps = f'(x) = 2x, g'(x) = cos(x), so (x²·sin(x))' = 2x·sin(x) + x²·cos(x)
Frequently Asked Questions
What is Product Rule Calculator?
- Product Rule Calculator evaluates Product Rule for the math / differentiation library. Primary input cue: First Function f(x) [required]: First function. Method anchor: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Product rule: derivative of first times second plus first times derivative of second. Product rule for differentiating pr.
How does Product Rule Calculator work?
- d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Product rule: derivative of first times second plus first times derivative of second. Product rule for differentiating product of two functions (calculator id: product-rule-calculator).
Why use this Math Numbers calculator?
- Use Product Rule Calculator when you already know the inputs and need product rule without setting up a spreadsheet.