Question

What is the derivative of `ln(x^3)`?

Answer 1

We can use the chain rule here, which states that

`(dy)/(dx)=(dy)/(du)(du)/(dx)`

Thus, as it's not possible to directly derivate `ln(x^3)`, we can rename `u=x^3` and proceed to derivate `ln(u)` following chain rule's steps.

`(dy)/(du)=1/u`
and
`(du)/(dx)=3x^2`

Now, aggregating both parts, as stated by the chain rule:

`(dy)/(dx)=1/u*3x^2=1/x^cancel(3)*3cancel(x^2)=color(green)(3/x)`