SUMMARY
The derivative of the function y = √x at x = 1 can be calculated using the limit definition of the derivative. The formula applied is lim x -> a = (f(x) - f(a)) / (x - a). By substituting f(x) with √x and simplifying the expression (√x - 1) / (x - 1), the derivative can be evaluated effectively. The final simplification leads to the result of 1/2, confirming that the derivative at x = 1 is 1/2.
PREREQUISITES
- Understanding of calculus concepts, specifically limits and derivatives.
- Familiarity with the limit definition of a derivative.
- Basic algebraic manipulation skills.
- Knowledge of square root functions and their properties.
NEXT STEPS
- Study the limit definition of derivatives in more detail.
- Practice derivative calculations for various functions using the limit approach.
- Explore the application of derivatives in real-world problems.
- Learn about higher-order derivatives and their significance.
USEFUL FOR
Students studying calculus, mathematics educators, and anyone interested in understanding the fundamentals of derivatives and their applications.