Question

Let f(x) = ln(1 + (1/x)). If g(x) = e^(2(f(x)), find g'(x). Leave answer in terms of e please!

Answer 1

PLEASE help me out guys!

Answer 2

\[e^{\ln(whatever)}=whatever\]

Answer 3

and also
\[e^{2\ln(\spadesuit)}=e^{\ln(\spadesuit^2)}=\spadesuit^2\]

Answer 4

therefore
\[\large e^{2\ln(1+\frac{1}{x})}=e^{\ln((1+\frac{1}{x})^2)}=(1+\frac{1}{x})^2\]

Answer 5

and since
\[(1+\frac{1}{x})^2=1+\frac{2}{x}+\frac{1}{x^2}\] taking the derivative should be okay