# proof of sum rule

$\frac{\mathrm{d}}{\mathrm{d}x}}\left[f(x)+g(x)\right]$ | $=$ | $\underset{h\to 0}{lim}{\displaystyle \frac{f(x+h)+g(x+h)-f(x)-g(x)}{h}}$ | ||

$=$ | $\underset{h\to 0}{lim}\left[{\displaystyle \frac{f(x+h)-f(x)}{h}}+{\displaystyle \frac{g(x+h)-g(x)}{h}}\right]$ | |||

$=$ | ${f}^{\prime}(x)+{g}^{\prime}(x)$ |

Title | proof of sum rule |
---|---|

Canonical name | ProofOfSumRule |

Date of creation | 2013-03-22 12:28:13 |

Last modified on | 2013-03-22 12:28:13 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 5 |

Author | mathcam (2727) |

Entry type | Proof |

Classification | msc 26A24 |

Related topic | Derivative |

Related topic | FixedPointsOfNormalFunctions |