Answer to Question #179766 in Calculus for Nora

Question

𝑓(𝑥) = 9 𝑙𝑜𝑔 (𝑥) + 12 ln (2𝑥 + 1)

Answer 1

Given  $f(x)=9 log⁡ x+12 ln⁡(2x+1)$

Which may be written as 

$f'(x)=d/dx [9lnx/ln10+12 ln⁡(2x+1) ]$

$=9/ln⁡10 (d(ln x))/dx+12 d[ln⁡(2x+1)]/dx$

$= 9/(xln 10)+12(2/(2x+1))$

$=9/(xln 10)+ 24/(2x+1)$