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Product Rule for Derivatives
Find the derivative of a function that is the product of two smaller functions, using a formula, worked examples, and clear steps.
What You'll Learn
The product rule lets you differentiate a function written as one function times another.
The formula is the derivative of the first times the second, plus the first times the derivative of the second.
You cannot just multiply the two individual derivatives together; that gives the wrong answer.
Worked examples show the rule applied to polynomial, trigonometric, and exponential factors.
The rule extends naturally to products of three or more functions.
Mixing up the product rule with the chain rule is one of the most common student errors.
What You'll Practice
1
Differentiating products of polynomials and trigonometric functions
2
Applying Product Rule with simple functions (no Chain Rule needed)
3
Combining Product Rule and Chain Rule for complex composite functions
4
Simplifying derivatives by bringing constants to the front
Why This Matters
The Product Rule is essential for calculus and appears constantly in physics, engineering, and economics when analyzing rates of change involving multiple varying quantities. Mastering this rule with the DOOD technique makes complex differentiation problems manageable throughout calculus.
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Product Rule
Differentiation
Chain Rule
Trigonometric Functions
Power Rule
Composite Functions
Calculus
GA Curriculum Aligned