# 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#

ExplanationSuppose,

#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#