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n.a.s.h
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Homework Statement
what is the derivative of e^[(-X^2-2x+1)/2]
Homework Equations
The Attempt at a Solution
Is this right?
= -(x+1)e^[(-x²-2x+1)]
Derivative of e^x with Exponential Functions - Homework Question and Solution
- Thread starter n.a.s.h
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- Derivative E^x
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SUMMARY
The derivative of the function e^[(-X^2-2x+1)/2] is correctly expressed as -(x+1)e^[(-x²-2x+1)/2]. The key to solving this derivative lies in applying the chain rule, specifically the formula [d/dx] e^f(x) = e^f(x) [d/dx] f(x). This method ensures accurate differentiation of exponential functions involving polynomial expressions.
PREREQUISITES- Understanding of exponential functions
- Familiarity with the chain rule in calculus
- Basic knowledge of derivatives
- Ability to manipulate polynomial expressions
- Study the chain rule in calculus in more detail
- Practice differentiating various exponential functions
- Explore applications of derivatives in real-world problems
- Learn about higher-order derivatives and their significance
Students studying calculus, particularly those focusing on derivatives of exponential functions, and educators looking for examples of applying the chain rule in differentiation.