SUMMARY
The derivative of the function f(x) = exp(-x^2) is correctly calculated using the chain rule. The proper differentiation yields f'(x) = -2x * exp(-x^2). The confusion arose from misapplying the chain rule, where the derivative of the inner function -x^2 must be multiplied by the outer function's derivative. The correct application of these rules leads to the final derivative expression without additional factors.
PREREQUISITES
- Understanding of basic calculus concepts, specifically differentiation.
- Familiarity with the chain rule in calculus.
- Knowledge of exponential functions and their properties.
- Ability to manipulate algebraic expressions involving derivatives.
NEXT STEPS
- Study the chain rule in detail to avoid common pitfalls in differentiation.
- Practice differentiating various exponential functions, particularly those involving polynomials.
- Explore applications of derivatives in real-world scenarios, such as optimization problems.
- Review examples of complex derivatives to strengthen understanding of differentiation techniques.
USEFUL FOR
Students learning calculus, educators teaching differentiation techniques, and anyone seeking to clarify the application of the chain rule in derivative calculations.