SUMMARY
The derivative of the function \( (1+4x)^5(3+x-x^2)^8 \) requires the application of both the product rule and the chain rule. The correct differentiation yields the expression \( 5(1+4x)^4(4)(3+x-x^2)^8 + 8(3+x-x^2)^7(1-2x)(1+4x)^5 \). It is crucial to ensure that both rules are applied correctly to avoid computational errors. Additionally, using LaTeX for mathematical expressions enhances clarity and presentation.
PREREQUISITES
- Understanding of the product rule in calculus
- Familiarity with the chain rule in calculus
- Knowledge of polynomial differentiation
- Ability to use LaTeX for mathematical notation
NEXT STEPS
- Practice applying the product rule with multiple functions
- Review chain rule applications in complex derivatives
- Explore LaTeX formatting for mathematical expressions
- Study polynomial functions and their derivatives in depth
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to improve their skills in differentiation techniques.