Confused on how the absolute value changes the method of deriving

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Homework Statement



Find derivative of abs (2x^3 + 8x^2 + 5x +1).

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The Attempt at a Solution



A little confused on how the absolute value changes the method of deriving that equation. When I derive it normally, I get (6x^2+16x+5).
 
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It might help to do simpler examples that you can graph - compare the derivative of abs(x) to the derivative of x or x2-1 vs abs(x2-1)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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