SUMMARY
The derivative of the function f(x) = (2 + 3sin(x))(4 + 5cos(x))tan(x) is calculated using the product rule. The correct derivative is f'(x) = (4 + 5)tan(x)(3cos(x)) + (2 + 3sin(x))(tan(x)(-5sin(x)) + sec²(x)(4 + 5cos(x))). This solution was confirmed by forum participants, with one user noting that WolframAlpha applies the product rule differently, leading to a potential simplification discrepancy.
PREREQUISITES
- Understanding of calculus, specifically differentiation techniques
- Familiarity with the product rule for derivatives
- Knowledge of trigonometric functions and their derivatives
- Experience using computational tools like WolframAlpha for verification
NEXT STEPS
- Study advanced differentiation techniques, including the product and chain rules
- Explore the properties and derivatives of trigonometric functions
- Learn how to use WolframAlpha for calculus problems
- Practice deriving complex functions involving multiple trigonometric terms
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to improve their skills in differentiation and trigonometric functions.