SUMMARY
The derivative of the function y = (2x² + 1)x^(1/2) is calculated using the Product Rule. The correct derivative is expressed as (10x² + 1)/(2√x). The initial attempt at differentiation resulted in (4x^(3/2) + 2x² + 1)/(2√x), indicating an algebraic error in combining terms. The key to resolving the issue lies in correctly applying the Product Rule and simplifying the expression by finding a common denominator.
PREREQUISITES
- Understanding of the Product Rule in calculus
- Familiarity with differentiation of polynomial functions
- Knowledge of simplifying algebraic fractions
- Basic proficiency in handling square roots and exponents
NEXT STEPS
- Review the Product Rule for differentiation in calculus
- Practice simplifying algebraic expressions involving square roots
- Explore examples of derivatives involving polynomial and radical functions
- Learn about common mistakes in algebraic manipulation during differentiation
USEFUL FOR
Students studying calculus, particularly those learning about differentiation techniques, as well as educators looking for examples of common errors in algebraic manipulation during calculus problems.