Question

\[{d \over dx} \ln {e^x \over 1+e^x}\]

Answer 1

d/dx(e^x/(1+e^x)/ [e^x/(1+e^x)] = [e^x(1+e^x)-e^x.(e^x) ] / [e^x/(1+e^x)]= 1+e^x

Answer 2

the quotient rule and the derivative of ln

Answer 3

\[\ln \frac{e^x}{1+e^x}=\ln(e^x)-\ln(1+e^x)\]

Answer 4

\[=x-\ln(1+e^x)\]

Answer 5

now its easy to differentiate

Answer 6

so the answer would be 1- (e^x)/(1+e^x)?

Answer 7

Yes, the answer is:
\[1-\frac{e^{x}}{1+e^{x}} \]

Answer 8

hmm, that's what I had at the beginning but i didn't get it on my calculator

Answer 9

\[x-\ln(1+e^x) =>1-\frac{1}{1+e^{x}} *e^x = 1-\frac{e^{x}}{1+e^{x}} = \frac{1+e^{x}-e^{x}}{1+e^{x}} = \frac{1}{1+e^{x}} \]

Answer 10

...oh. could've done that I guess :P
Thanks, all!