Derivatives of Products and Quotients!!

If f(x) = r(x)^{ .}s(x) and if both derivatives exist, then

f '(x) = r(x)^{.}s'(x) + s(x)^{.}r'(x)

In words, this means the derivative of a product is the first function times the derivative of the second function plus the second function times the derivative of the first function!!

r(x) = 3x^{2} |
s(x) = 5x^{2} - 3x |

r'(x) = 6x | s'(x) = 10x - 3 |

*Set up a chart like
the one
above. Then cross multiplying the values in the chart will give
you
f'(x)*

r(x) = 2x - 1 | s(x) = 3x + 2 |

r'(x) = 2 | s'(x) = 3 |

r(x) = x^{1/2} + 2 |
s(x) = x^{2} - 3x |

r'(x) = 1/2x^{1/2} |
s'(x) = 2x - 3 |

r(x) = 2x - 1 | s(x) = 3x + 4 |

r'(x) = 2 | s'(x) = 3 |

r(x) = 3 - 4x | s(x) = 5x + 1 |

r'(x) = -4 | s'(x) = 5 |

r(x) = (3 - 4x)(5x + 1) | s(x) = (7x - 9) |

r'(x) = 11 - 40x | s'(x) = 7 |