The reason the absolute value is given in the question is simply because the logarithm of a negative number does not exist. So, you should write your answer as:
Hope that helps!
I am slowly moving through the calculus portion of a math textbook my girlfriend lent me and am stuck on a few problems involving finding the first derivative of equations involving absolute values.
I will use one of these as an example.
Find the derivative of:
Normally, if there was no absolute value, I would rewrite the equation as . Then I would use the product rule to get . Likely ending up writing it as .
*I did this to show that I know how to do it with no absolute value*
I know what an absolute value is, I am unsure of what to do with it when trying to derive a function that has one.
I searched google and found a couple websites that tried to explain it, but I could not grasp what they were saying. I was hoping that someone could, using my example, explain (in english) how to go about doing this.
Thanks in advanced!