Question

what is the derivative of ln(1+1/x)?
they say the answer is xsquared-1/ xcubed+x
now can someone explain how you find the answer

Answer 1

the answer given is correct but not simplified....
use the formula \(\large [lny]'=\frac{y'}{y} \) to find the derivative...

Answer 2

then how do i use this formula for the problem

Answer 3

let \(\large y=1+\frac{1}{x} \)
so,
\(\large [ln(1+\frac{1}{x})]'=\frac{[1+\frac{1}{x}]'}{1+\frac{1}{x}} \)

can you find \(\large [1+\frac{1}{x}]'= \) ????

Answer 4

no how do u find 1+1/x?
is the answer -1x-1/2

Answer 5

use the sum rule for derivatives...
\(\large [1+\frac{1}{x}]'=[1]'+[\frac{1}{x}]' \)

continue....

Answer 6

??

Answer 7

ok... good...
so,
\(\large [ln(1+\frac{1}{x})]'=\frac{[1+\frac{1}{x}]'}{1+\frac{1}{x}}=\frac{-x^{(\frac{-1}{2})}}{1+\frac{1}{x}} \)

now just simplify...

Answer 8

wait but how do i simplify to get ...