HEY .....................

LOOK...........

FOR the differentition of   log x

use first principles which says,,,,,,,,,

lim       [ f(x+h)  -   f(x)]/  h

h->0

now put f(x)= log x...........we get........

lim     [ log(x+h)  -  log(x)]/h

h-->0

lim     [  log{ x(1 + h/x)} -  logx  ]/h

h-->0

lim   [  log x  +   log( 1+ h/x)  -  log x]   /h

h-->0

lim     log (1+  h/x) /  h    

h-->0

now   as we know...........log(1+h)/h  =1   ( where h-->0)

therefore applying ......we get...................

multiplying denominator by x and dicviding by x................

we get.............

 

lim   log(1+  h/x)  /  (xh/x)                 (  as log ( 1+ h/ x) / (h/x)   =1)

h-->0

therefore we get

lim 1/x

h-->0

=  1/x  (ans)

thanku..........

hope u have understood it............