What the product rule says
You cannot differentiate a product by multiplying the separate derivatives alone. The correct identity is (fg)′ = f′g + fg′. A product rule calculator expands both terms and labels the rule so you can check each half of your written solution.
Always write both factors before differentiating. A common error is computing only f′g and forgetting fg′ when one factor “looks easy.”
How to use this product rule derivative calculator
- Enter a product with
*between factors (e.g.x^2*sin(x)). - Press Calculate and locate the product-rule step.
- Verify each factor’s derivative, including any chain-rule pieces.
- Compare the simplified sum with your homework answer.
Product rule practice set
x^2*sin(x)— polynomial times trigx*e^x— classic textbook productx*ln(x)— product with a logsin(x)*cos(x)— two trig factorsx^3*e^(2*x)— product plus chain on the exponential(x+1)*sqrt(x)— linear times root
Products nested with other rules
When a factor is a quotient or a composition, the step list stacks rules: product on the outside, chain or quotient inside. For pure quotients, prefer the quotient rule calculator. For pure compositions, use the chain rule calculator.
Evaluating the derivative afterward at a number? Continue with the derivative at a point calculator workflow after you trust f′(x).
Product rule calculator FAQ
What is the product rule?
(fg)′ = f′g + fg′ — differentiate one factor at a time and add.
How do I use this calculator?
Enter a product, Calculate, and read the labeled product-rule steps under the result.
Is it free?
Yes — free steps with no account.
What if a factor needs the chain rule?
The engine applies chain inside the product terms. Try x*sin(x^2).