Derivative of compound interest

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SUMMARY

The discussion focuses on finding the derivative of the function f(x) = (1/x + 1)^x. The correct approach involves using the exponential form f(x) = exp(ln(1/x + 1) * x) to facilitate differentiation. Participants clarify that the derivative of a^x is ln(a) * a^x, emphasizing that 'a' must be a constant. The application of the chain rule is crucial in the differentiation process, which resolves the initial confusion regarding the derivative calculation.

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  • Understanding of derivatives and differentiation rules
  • Familiarity with exponential functions and logarithms
  • Knowledge of the chain rule in calculus
  • Basic algebraic manipulation skills
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  • Study the application of the chain rule in calculus
  • Learn about logarithmic differentiation techniques
  • Explore the properties of exponential functions
  • Practice finding derivatives of composite functions
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Students studying calculus, mathematics educators, and anyone interested in mastering differentiation techniques, particularly in the context of exponential functions.

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Homework Statement


f(x) = (1/x+1)^x, find f'(x)


Homework Equations


derivative of a^x = ln(a) a^x


The Attempt at a Solution


When I differentiate i get ln((1+x)/x)*((1+x)/x)^x... However, this solution does not match what I should be getting. Am i differentiating wrong at some point? or are my notes that claim a^x = lna*a^x wrong...
 
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Your formula for a^x assumes a is a constant. The easiest way to handle this one is to use (1/x+1)=exp(ln(1/x+1)) so f(x)=exp((ln(1/x+1))*x). Now just differentiate and don't forget the chain rule.
 
duh!


thanks so much dick I can't believe I stared at it for that long and didn't realize that.
 

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