How do you use the quotient rule to find the derivative of #y=x/ln(x)# ?
1 Answer
Aug 13, 2014
#y'=(lnx-1)/(lnx)^2# Explanation
Suppose,
#y=f(x)/g(x)# Using Quotient Rule, which is
#y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2# Similarly, following for the given problem
#y=x/lnx# and differentiating with respect to#x# , yields
#y'=((x)'(lnx)-x(lnx)')/(lnx)^2#
#y'=(lnx-x*1/x)/(lnx)^2#
#y'=(lnx-1)/(lnx)^2#
