# How do you differentiate #f(x)=(1-lnx)/(1+lnx)# using the quotient rule?

##### 1 Answer

Oct 30, 2017

# d/dx (1-lnx)/(1+lnx) = - ( 2 ) / ( x(1+lnx)^2 )#

#### Explanation:

Using the quotient rule, we have:

# d/dx (1-lnx)/(1+lnx) = ( (1+lnx)(d/dx (1-lnx)) - (1-lnx)(d/dx(1+lnx)) ) / (1+lnx)^2#

# " " = ( (1+lnx)(-1/x) - (1-lnx)(1/x) ) / (1+lnx)^2#

# " " = ( (-1/x)( 1+lnx + 1-lnx) ) / (1+lnx)^2#

# " " = ( (-1/x)( 2) ) / (1+lnx)^2#

# " " = - ( 2 ) / ( x(1+lnx)^2 )#