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

1 Answer
Dec 25, 2015

We'll need the chain rule here, which states that (dy)/(dx)=(dy)/(du)(du)/(dx)

Explanation:

In this case, we must rename u=(1/x) and now derivate the function y=lnu. Let's do it separately, step-by-step:

(dy)/(du)=1/u

(du)/(dx)=-1/x^2

(dy)/(dx)=-1/(ux^2)

Substituting u:

(dy)/(dx)=-1/((1/x)x^2)=-1/x