# Thread: Derivatives involving absolute values

1. ## Derivatives involving absolute values

Hey,

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.

Question
Find the derivative of: $\displaystyle y = \frac{ln|x|}{x^4}$

Solution
Normally, if there was no absolute value, I would rewrite the equation as $\displaystyle (lnx)(x^{-4})$. Then I would use the product rule to get $\displaystyle (\frac{1}{x})(x^{-4}) + (-4x^{-5})(lnx)$. Likely ending up writing it as $\displaystyle \frac {x}{x^4} + \frac {-4lnx}{x^5}$.
*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.
$\displaystyle (\frac{1}{x})(x^{-4})+(-4x^{-5})(ln|x|)$
$\displaystyle \frac {1}{x^5}-\frac {4}{x^5}ln|x|$