Question

in ln|x| would the absolute value make any difference?

Answer 1

when calculating a derivative***

Answer 2

this normally is there to make sure x is always positive

Answer 3

Nope it'd be the same
\[\frac1 x\]

Answer 4

changing from
\[\ln(x)\] to \[\ln(|x|)\]changes the domain from \((0,\infty)\) to all real numbers except 0

Answer 5

the domain now will be all reals except x=0 and the derivative will be -1/x for x<0