Question

How do you find the derivative of `f(x)=ln(3x^(2)+6x+5)`?

Answer 1

`(6(x+1))/(3x^(2)+6x+5)`

Explanation:

`f(x)=ln(3x^(2)+6x+5)`

as a general matter if `y = ln ( f(x) )` then `y' = 1/(f(x)) f'(x)` [chain rule]

here `f'(x)=1/(3x^(2)+6x+5)(3x^(2)+6x+5)'`
`=(6x+6)/(3x^(2)+6x+5)`