What is the derivative of #f(x)=ln(x)/x# ?

1 Answer
Sep 22, 2014

By Quotient Rule,

#y'={1/x cdot x-lnx cdot 1}/{x^2}={1-lnx}/{x^2}#

This problem can also be solved by the Product Rule

#y'=f'(x)g(x)+f(x)g(x)#

The original function can also be rewritten using negative exponents.

#f(x)=ln(x)/x=ln(x)*x^-1#

#f'(x)=1/x*x^-1+ln(x)*-1x^-2#

#f'(x)=1/x*1/x+ln(x)*-1/x^2#

#f'(x)=1/x^2-ln(x)/x^2#

#f'(x)=(1-ln(x))/x^2#