SUMMARY
The derivative of the function f(x) = 3 - (3/5)x is calculated using the power rule. The constant term 3 has a derivative of 0, while the term involving x is rewritten as (3/5)x^-1. Applying the power rule results in f'(x) = -3/5x^-2, which can be expressed with positive exponents as f'(x) = 3/(5x^2). This process demonstrates the application of differentiation techniques for polynomial functions.
PREREQUISITES
- Understanding of basic calculus concepts, specifically derivatives.
- Familiarity with the power rule of differentiation.
- Knowledge of rewriting expressions with negative exponents.
- Ability to manipulate algebraic expressions involving fractions.
NEXT STEPS
- Study the application of the power rule in more complex functions.
- Learn about the implications of constant derivatives in calculus.
- Explore the concept of rewriting expressions for easier differentiation.
- Investigate common mistakes in derivative calculations and how to avoid them.
USEFUL FOR
Students learning calculus, educators teaching differentiation techniques, and anyone seeking to improve their understanding of polynomial derivatives.