SUMMARY
The derivative of the function g(x)=(2x+1)^2(x-7)^3 is calculated using the product rule, resulting in the expression 4(2x+1)(x-7)^3 + 3(2x+1)^2(x-7)^2. To factor this expression into its final form, 5(x-7)^2(2x-5)(2x+1), one must first identify common factors and combine terms appropriately. The key steps involve recognizing the common factor (2x+1)(x-7)^2 and simplifying the remaining terms within the brackets.
PREREQUISITES
- Understanding of the Product Rule in calculus
- Familiarity with the Chain Rule in calculus
- Ability to perform polynomial factoring
- Knowledge of basic algebraic manipulation
NEXT STEPS
- Study the application of the Product Rule in calculus
- Learn advanced factoring techniques for polynomials
- Practice finding derivatives of composite functions using the Chain Rule
- Explore examples of combining like terms in algebraic expressions
USEFUL FOR
Students studying calculus, particularly those learning about derivatives and the application of the Product Rule, as well as educators seeking to clarify these concepts for their students.