SUMMARY
The derivative of the function 3(2x² + 1) is confirmed to be 12x. The differentiation process can be approached in two ways: first by applying the power rule directly to the expression, resulting in 4x.3(2x² + 1)⁰, which simplifies to 12x, or by first expanding the expression to 6x² + 3 and then differentiating to arrive at the same result. Both methods yield the same derivative, affirming the correctness of the solution provided by the user.
PREREQUISITES
- Understanding of basic calculus concepts, specifically differentiation.
- Familiarity with the power rule of derivatives.
- Knowledge of polynomial functions and their properties.
- Ability to simplify algebraic expressions.
NEXT STEPS
- Study the power rule of differentiation in more depth.
- Learn about the product rule for differentiating products of functions.
- Explore the chain rule for differentiating composite functions.
- Practice differentiating more complex polynomial functions.
USEFUL FOR
Students in calculus courses, mathematics educators, and anyone looking to strengthen their understanding of differentiation techniques.