Confused on how the absolute value changes the method of deriving

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SUMMARY

The discussion focuses on finding the derivative of the absolute value function abs(2x^3 + 8x^2 + 5x + 1). The standard derivative of the polynomial is calculated as (6x^2 + 16x + 5). However, the presence of the absolute value necessitates a different approach, particularly when considering the behavior of the function at points where the polynomial equals zero. The participants suggest using simpler examples, such as comparing the derivatives of abs(x) and x, to illustrate the impact of absolute values on differentiation.

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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)
 

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