SUMMARY
The derivative of the function arcsin(4x+2) is calculated as 4 / (√(1 - (4x + 2)²)). The initial confusion regarding the expression arose from a typographical error where (4x - 2) was mistakenly used instead of the correct (4x + 2). Tools such as Wolfram Integrals and Calc101 can be utilized for verification of derivatives and exploring alternative methods of simplification.
PREREQUISITES
- Understanding of calculus concepts, specifically derivatives.
- Familiarity with the arcsine function and its properties.
- Knowledge of the chain rule in differentiation.
- Basic skills in using online mathematical tools for verification.
NEXT STEPS
- Study the chain rule in calculus for better understanding of derivative calculations.
- Explore the properties of inverse trigonometric functions, particularly arcsin.
- Learn how to use Wolfram Alpha for checking derivatives and integrals.
- Investigate common mistakes in derivative calculations and how to avoid them.
USEFUL FOR
Students studying calculus, particularly those learning about derivatives of inverse trigonometric functions, and anyone seeking to verify their mathematical solutions using online tools.