F(x)=xabs(x) show f '(0) exists

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f(x)=xabs(x) show f '(0) exists
 
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What have you tried so far. You'll have to show some work first showing you attempted it before we can help you.
 
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Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

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