SUMMARY
The derivative of the function y = (1/x) + sqrt(cos x) was evaluated at the point (pi/2, 2/pi). The power rule was applied to (1/x) and the chain rule to sqrt(cos x). The derivative becomes undefined at x = pi/2 due to the square root of cos(x) being negative in certain intervals, which restricts the domain of the function. The discussion emphasizes the importance of analyzing the domain of the derivative to avoid confusion regarding undefined values.
PREREQUISITES
- Understanding of calculus concepts such as derivatives and rules (power rule, chain rule)
- Familiarity with trigonometric functions, specifically cosine
- Knowledge of domain restrictions for functions involving square roots
- Ability to evaluate limits and continuity in calculus
NEXT STEPS
- Study the application of the power rule in calculus
- Learn about the chain rule and its implications for composite functions
- Investigate the properties of the cosine function and its impact on square roots
- Explore domain restrictions and how to identify them in various functions
USEFUL FOR
Students studying calculus, particularly those focusing on derivatives, as well as educators seeking to clarify concepts related to function domains and trigonometric functions.