Question

What are the first and second derivatives of `f(x)=ln (6^x)`?

Answer 1

We'll resort to chain rule here.

Explanation:

Chain rule states that `(dy)/(dx)=(dy)/(du)(du)/(dx)`

Renaming `u=6^x`, we can start:

`(dy)/(du)=1/u`

`(du)/(dx)=6^xln(6)*1=6^xln(6)`

`(dy)/(dx)=(6^x*ln(6))/6^x=ln(6)`

As `ln(6)` is a constant, its derivative is zero.