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Calculus/differentiation

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Expert: - 1/19/2011


Question
what is the derivative of the nth power of absolute value of x?or simply derivative of absolute value of a real value x?

Answer
If f(x) = |x|, then f'(x) = 1 for x>0 and f'(x) = -1 for x < 0.
At 0, f'(x) is not defined.
From here, f"(x) = 0 at all points besides x=0.
From this, it can be seen that the nth derivative at any point is 0 if n>=2 and x!=0.

See, in C++, != is used for 'not equal to'.

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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