Question

Find the derivative and simplify your answer as much as possible.

Answer 1

\[f(x) = \ln(2+lnx)\]

Answer 2

Find \[f'(\frac{1}{e})\]

Answer 3

f'(x) = .... ?

Answer 4

chain rule

Answer 5

I used it and got \[\frac{1}{x(2+lnx)}\]

Answer 6

correct, just plug in x = 1/e
and use the fact that ln e =1

Answer 7

but look at this\[\frac{1}{(\frac{1}{e}*(2+\ln(\frac{1}{e}))}\]

Answer 8

ln (1/A) = ln A^-1 = -ln A

Answer 9

by the property that \(\Large \log y^x =x\log y \)

Answer 10

So it all comes to become e

Answer 11

correct :)