What is the derivative of ##y=ln(1/x)##?

##y'=-1/x##

Full solution

##y=ln(1/x)##

This can be solved in two different ways,

Explanation (I)

The simplest one is, using logarithm identity,

##log(1/x^y)=log(x^-y)=-ylog (x)##, similarly following for problem,

##y=-ln(x)##

##y'=-(ln(x))'##

##y'=-1/x##

Explanation (II)

Using ,

##y'=(ln(1/x))'##

##y'=1/(1/x)*(-1/x^2)=-1/x##

##y'=-1/x##