Derivative of compound interest

[lax1113]

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...

 

[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.