SUMMARY
The derivative of the function h(x) = (sin(2x))(cos(2x)) can be calculated using the product rule combined with the chain rule. The correct derivative is 2cos(4x), which aligns with the answer provided in the textbook. The error in the initial attempt stemmed from neglecting the chain rule when differentiating cos(2x), where the derivative is -2sin(2x). Additionally, utilizing trigonometric identities such as cos(2u) = cos²(u) - sin²(u) can simplify the process.
PREREQUISITES
- Understanding of the product rule in calculus
- Knowledge of the chain rule in differentiation
- Familiarity with trigonometric identities
- Basic proficiency in calculus, particularly derivatives of trigonometric functions
NEXT STEPS
- Study the application of the product rule in calculus
- Learn the chain rule and its implications in differentiation
- Explore trigonometric identities and their uses in calculus
- Practice finding derivatives of composite functions involving trigonometric functions
USEFUL FOR
Students studying calculus, particularly those focusing on derivatives of trigonometric functions, as well as educators seeking to clarify the application of differentiation rules.