Product Rule — SymPy
Verified Calculation Engine
The online Product Rule — SymPy 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.
Differentiate a product of symbolic functions.
(fg)' = f'g + fg'.
Differentiate a product of symbolic functions.
Inputs
Results
Worked Examples
Validated worked example
Product rule
- f: x^2
- g: sin(x)
- derivative: x**2*cos(x) + 2*x*sin(x)
About this calculator
Overview
Product Rule — SymPy evaluates Product Rule — SymPy for the math / differentiation library. Primary input cue: f(x) [required]. Method anchor: (fg)' = f'g + fg'.. Differentiate a product of symbolic functions..
When to use
Use Product Rule — SymPy when you already know the inputs and need product rule — sympy without setting up a spreadsheet.
Inputs explained
- f(x) [required]
- g(x) [required]
Formula / method
(fg)' = f'g + fg'.. Differentiate a product of symbolic functions (calculator id: product-rule-symbolic-v3-calculator).
Worked example
Worked values: f = x^2, g = sin(x) → derivative = x**2*cos(x) + 2*x*sin(x)
Interpreting results
Read the primary output as product rule — sympy under the method on this page.
Assumptions
- Units (when shown) must be consistent across inputs for product rule — sympy. [product-rule-symbolic-v3-calculator]
- Empty required inputs are not silently replaced with zeros for product rule — sympy.
- Real-number arithmetic is used unless product rule — sympy explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to product rule — sympy.
- Product Rule — SymPy cannot invent missing inputs; incomplete forms stop short of a forged product rule — sympy value.
- Complex/branch cuts and undefined points are not always interactively annotated for product rule — sympy.
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
(fg)' = f'g + fg'.. Differentiate a product of symbolic functions (calculator id: product-rule-symbolic-v3-calculator).
Example Calculation
Worked values: f = x^2, g = sin(x) → derivative = x**2*cos(x) + 2*x*sin(x)
Frequently Asked Questions
What is Product Rule — SymPy?
- Product Rule — SymPy evaluates Product Rule — SymPy for the math / differentiation library. Primary input cue: f(x) [required]. Method anchor: (fg)' = f'g + fg'.. Differentiate a product of symbolic functions..
How does Product Rule — SymPy work?
- (fg)' = f'g + fg'.. Differentiate a product of symbolic functions (calculator id: product-rule-symbolic-v3-calculator).
Why use this Math Numbers calculator?
- Use Product Rule — SymPy when you already know the inputs and need product rule — sympy without setting up a spreadsheet.