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K29
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Homework Statement
I have proven in two ways (correctly) that the derivative of ln|x| = 1/x (note absolute value does vanish)
Now I open my textbook and see a general rule that [tex]\frac{d}{dx} ln (u) = \frac{u'}{u}[/tex]
And the not so general derivative of |x| is [tex] \frac{d}{dx} |x| = \frac{x}{|x|}[/tex]
So using these statements [tex]\frac{d}{dx} ln (|x|) = \frac{|x|'}{|x|}[/tex]
[tex]=\frac{(\frac{x}{|x|})}{|x|}[/tex]
[tex]=\frac{x}{|x|^{2}}[/tex]
I've looked over this a few times and I can't see what I've done wrong. I mean I'm looking for a silly mistake but I don't see it. Can you see where I've gone wrong? Whats going on here?
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