Given the function $f(x)=ln(x^2-14x)$, find the derivative and the domain of f.
I found the derivative to be $\frac{2(x-7)}{x(x-14)}$ which was correct. I then tried to find the domain by finding where the denominator was equal to zero, which is at x=0 and x=14. I thought that the domain would be (-infinity, 0), (0, 14), (14, infinity), but the correct domain is without the (0, 14). I don't understand why (0, 14) is not in the domain, can somebody help explain it to me?
The question asks for the domain of $f$, not $f'$, so you must decide where $$ f(x)=\ln(x^2-14x) $$ makes sense or where $$ x^2-14x>0\Rightarrow x<0\;\text{or}\;x>14 $$