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

1 Answer
Oct 18, 2016

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)