Equation with absolute value

Equation with absolute value

Input
abs(x)
Alternate form assuming x is positive
x
Alternate form assuming x is real
sqrt(x^2)
Root
x = 0
Derivative
d/dx(abs(x)) = x/(abs(x))
(assuming a function from reals to reals)
Indefinite integral assuming all variables are real
integral abs(x) dx = 1/2 x^2 sgn(x) + constant
Global minimum
min{abs(x)} = 0 at x = 0

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