SUMMARY
The discussion confirms the correctness of the derivative solution for the function 2sin(x)cos(x). The initial attempt at a solution, which resulted in (2cos(x)cos(x)) - (2sin(x)sin(x)), is validated but recommended for simplification to 2cos²(x) - 2sin²(x). This expression is recognized as a trigonometric identity, specifically 2cos(2x), which could have been derived more efficiently by applying the identity 2sin(x)cos(x) = sin(2x) directly.
PREREQUISITES
- Understanding of basic trigonometric identities
- Knowledge of differentiation techniques in calculus
- Familiarity with the product rule in derivatives
- Ability to simplify trigonometric expressions
NEXT STEPS
- Study the derivation of trigonometric identities, particularly sin(2x) and cos(2x)
- Learn about the product rule in calculus for differentiating products of functions
- Practice simplifying trigonometric expressions using identities
- Explore advanced differentiation techniques, including implicit differentiation
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of trigonometric derivatives and identities.