SUMMARY
The derivative of the function (x^2-6x+9)(2x^2-x+1) is confirmed to be 8x^3 - 39x^2 + 50x - 15. The initial calculation included a miscalculation in the distribution of terms, particularly with the "4x" times "9" term. The correct application of the product rule and simplification leads to the final result, ensuring accuracy in polynomial differentiation.
PREREQUISITES
- Understanding of the product rule in calculus
- Familiarity with polynomial functions
- Ability to perform algebraic simplification
- Knowledge of derivative notation and rules
NEXT STEPS
- Review the product rule for derivatives in calculus
- Practice polynomial differentiation with various functions
- Learn about common mistakes in derivative calculations
- Explore advanced topics in calculus such as implicit differentiation
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to improve their skills in polynomial differentiation and derivative calculations.