If y= (x-1)log(x-1)-(x+1)log(x+1), prove that dy/dx = log(x-1/1+x)

Answer 1

use the product rule

dy/dx = (x-1)(1/(x-1)) + log(x-1) - [ (x+1)(1/(x+1)) + log(x+1) ]
= 1 + log(x-1) - 1 - log(+1)
= log [(x-1)/(x+1)]

= RS , had you typed it correctly as log((x-1)/(1+x))