Product Rule Calculator
Find the derivative of the product of two functions. Get instant step-by-step solutions — completely free, no signup required.
Free Product Rule Calculator Calculator
Enter your problem below to get an instant step-by-step solution.
About Product Rule Calculator
Find the derivative of the product of two functions. Calculus is the mathematical study of continuous change. It provides tools for analyzing functions, computing areas and volumes, and solving differential equations that model real-world phenomena.
Our Product Rule Calculator calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any product rule calculator expression and receive a complete, verified solution with every step shown.
Product Rule Calculator Formula
d/dx [f·g] = f′g + fg′
The product rule differentiates two functions multiplied together. The derivative of a product is not the product of the derivatives: each factor takes a turn being differentiated while the other stays the same, and the two results are added.
Worked Example
Differentiate y = x³ · sin(x)
- f = x³, f′ = 3x²
- g = sin(x), g′ = cos(x)
- Apply the rule: y′ = 3x² sin(x) + x³ cos(x)
- Factor out x²: y′ = x²(3 sin x + x cos x)
Answer: y′ = x²(3 sin x + x cos x)
Common Mistakes to Avoid
- Writing (fg)′ = f′g′.
- Missing the chain rule when one factor is itself a composite such as sin(2x).
- Expanding a simple polynomial product with the rule when multiplying out first is faster.
How to Use the Product Rule Calculator Calculator
- 1
Enter your calculus expression (e.g., a function for Product Rule Calculator) into the input field
- 2
Press Enter or click the Solve button to run the calculation
- 3
Review the step-by-step solution that appears below the input
- 4
Check the breakdown of each operation to understand the method
- 5
Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Product Rule Calculator formula?
d/dx [f·g] = f′g + fg′. The product rule differentiates two functions multiplied together. The derivative of a product is not the product of the derivatives: each factor takes a turn being differentiated while the other stays the same, and the two results are added.
Can you show a worked Product Rule Calculator example?
Differentiate y = x³ · sin(x): f = x³, f′ = 3x²; g = sin(x), g′ = cos(x); Apply the rule: y′ = 3x² sin(x) + x³ cos(x); Factor out x²: y′ = x²(3 sin x + x cos x). Answer: y′ = x²(3 sin x + x cos x).
Is this Product Rule Calculator calculator free to use?
Yes — the Product Rule Calculator calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Product Rule Calculator homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.
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