# Derivative 4e^x

Derivative |
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d/dx(4 e^x) = 4 e^x |

Roots |

(no roots exist) |

Periodicity |

periodic in x with period 2 i pi |

Series expansion at x=0 |

4 + 4 x + 2 x^2 + (2 x^3)/3 + x^4/6 + O(x^5) (Taylor series) |

Indefinite integral |

integral 4 e^x dx = 4 e^x + constant |

Limit |

lim_(x->-infinity) 4 e^x = 0 |

Definite integral |

integral_(-infinity)^0 4 e^x dx = 4 |

Definite integral over a half-period |

integral_0^(i pi) 4 e^x dx = -8 |