# 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 |