Question

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

Answer 1

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`