TITLE: How is this function never decreasing?!
QUESTION [6 upvotes]: What I'm doing is finding where this function is decreasing or increasing. 
Here is the original function:
$f(x) = \ln(x+6)-2$
I take the prime when I believe is:
$f'(x)= \dfrac{1}{x+6}$
Then I made a sign chart. 
I know right off the bat that there is nothing that make this function equal to zero because the numerator doesn't have an $x.$
The denominator can make the function undefined, and it's undefined at $-6.$ So thats the number I use on my sign chart.
I plugged the first value $-10$ into the prime function and it gives me a negative value:
$f'(-10)= \frac{1}{(-10+6)}$
$ = \frac{-1}{4}$
Then I plugged the $0$ in and I got
$f'(0)= 1/6$
It should look something like this:
   -          n | d         +

-----(-10)------ ((-6)) -------(0)------
My homework is saying the function is never decreasing. >.

REPLY [2 votes]: The function $\ln(x+6)$ is the inverse function of the strictly increasing function $g(x)=e^x-6$.
(We have $y=\ln(x+6)$ if and only if $e^y=x+6$ if and only if $x=e^y-6$.)