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# Calculus - Exam 2

### Derivatives, etc.

Question | Answer |
---|---|

d/dx[k] (k = constant) | 0 |

d/dx[x^n] | nx^(n-1) |

d/dx[f(x)±g(x)] | f^1(x)±g^1(x) |

d/dx[f(x)g(x)] | f^1(x)g(x)+f(x)g^1(x) |

d/dx[f(x)/g(x)] | (lodehi - hidelo)/lolo (lo^2) |

d/dx[e^x] | e^x |

d/dx[ln(x)] | 1/x |

d/dx[sin(x)] | cos(x) |

d/dx[cos(x)] | -sin(x) |

d/dx[k f(x)] | k f^1(x) |

d/dx[tan(x)] | sec^2(x) |

d/dx[cot(x)] | -csc^2(x) |

d/dx[sec(x)] | sec(x)tan(x) |

d/dx[csc(x)] | -csc(x)cot(x) |

d/dx[loga(x)] | 1/(xln(a)) |

loga(x) | ln(x)/ln(a) |

d/dx[arctan(x)] | 1+x^2 |

d/dx[arcsin(x)] | 1/(sqrt(1-x^2)) |

f^1(x) | (f(x+h)-f(x))/h |

Average Rate of Change | (f(x2)-f(x1))/(x2-x1) |

Relative Rate of Change | f^1(x)/f(x) |

Falling Body Formula | -(1/2)gt^2 + v0t + s0 |

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