Question

What is the derivative of `ln(2x+1)`?

Answer 1

`2/(2x+1)`

Explanation:

`y=ln(2x+1)` contains a function within a function, i.e. `2x+1` within `ln(u)`. Letting `u=2x+1`, we can apply chain rule.

Chain rule: `(dy)/(dx)=(dy)/(du)*(du)/(dx)`

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

`(du)/(dx)=d/(dx)2x+1=2`

`:.(dy)/(dx)=1/u*2=1/(2x+1)*2=2/(2x+1)`