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 )#
