Question

derivative of ln(x).

Answer 1

ln|x| is 1/x. so what is derivative of ln(x)?

Answer 2

still 1/x... as long as x >0

Answer 3

ok, so what is antiderivative of 1/|x|

Answer 4

abs value confuses me

Answer 5

antiderivative of 1/|x| ??? where did that come from

Answer 6

i meant integral of 1/|x| = ? it's a diff. question.

Answer 7

@alienbrain , on your first post, what do you mean by "ln|x| is 1/x"

Answer 8

i meant to say, the derivative of ln|x| is 1/x.

Answer 9

the point of all of this is to clarify when to use abs value

Answer 10

I think you have something confused\[\int\frac{dx}x=\ln|x|+c\]but\[\frac d{dx}(\ln x)=\frac1x\]

Answer 11

the antiderivative would be:
-ln(-x) when x<0
ln(x) when x>0