Derivative of compound interest

[lax1113]

1. The problem statement, all variables and given/known data
f(x) = (1/x+1)^x, find f'(x)


2. Relevant equations
derivative of a^x = ln(a) a^x


3. 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...

[Dick]

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.

[lax1113]

duh!!!!


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