Given f(x)=(1+1/x)^x ,find f'(x) ?
Answers
Answered by
0
Hi Mate !!!
F ( x ) = ( 1 + 1/x ) ^ x
Taking log on both sides
Log ( F ( x ) ) =. x Log ( 1 + 1/x)
Now differentiate both sides with respect to x
{ 1 / F ( x ) } × F ' ( x ) = {Log ( 1 + 1/x ) + x ( 1 / 1+
(1/x) × - 1/x²}
F ' ( x ) = F ( x ) { Log ( 1 + 1/x + x ( 1/ 1+ 1/x × -1/x²}
Now it is a simple algebra as u can do it by own
Hope it helps....
F ( x ) = ( 1 + 1/x ) ^ x
Taking log on both sides
Log ( F ( x ) ) =. x Log ( 1 + 1/x)
Now differentiate both sides with respect to x
{ 1 / F ( x ) } × F ' ( x ) = {Log ( 1 + 1/x ) + x ( 1 / 1+
(1/x) × - 1/x²}
F ' ( x ) = F ( x ) { Log ( 1 + 1/x + x ( 1/ 1+ 1/x × -1/x²}
Now it is a simple algebra as u can do it by own
Hope it helps....
Similar questions