SUMMARY
The derivative of the function f(x) = sin(x)cos(x) can be calculated using the Product Rule, resulting in f'(x) = cos^2(x) - sin^2(x) or equivalently f'(x) = (1/2)sin(2x). The initial attempt at differentiation led to an incorrect conclusion that the derivative equals zero, which is not valid as sin(x)cos(x) is not a constant function. Recognizing trigonometric identities is crucial for simplifying the derivative correctly.
PREREQUISITES
- Understanding of the Product Rule in calculus
- Familiarity with trigonometric identities, specifically sin(2x)
- Basic differentiation techniques
- Knowledge of how to manipulate trigonometric functions
NEXT STEPS
- Study the Product Rule in more depth with examples
- Learn about trigonometric identities and their applications in calculus
- Explore the concept of derivatives of composite functions
- Practice problems involving the differentiation of trigonometric products
USEFUL FOR
Students studying calculus, particularly those focusing on differentiation techniques and trigonometric functions, as well as educators looking for clear examples of applying the Product Rule.