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Math Help - Differentiation

  1. #1
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    Differentiation

    Find (\frac{r_1}{|r_2| } )' for  r_1 = ti + {t}^{ 2} j - 3tk and r_2 = {t}^{ 2}i - 2j + tk

    I have found |r_2| = \sqrt{{t}^{ 4} + {t}^{2 } + 4  }

    But now when i differntaite i do not get there answer of

     <br />
\frac{4-{t}^{4}i}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }}  }+ \frac{{t}^{3}+ 8tj}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }} +  \frac{3({t}^{4}-4k}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }   }<br />
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by adam_leeds View Post
    Find (\frac{r_1}{|r_2| } )' for  r_1 = ti + {t}^{ 2} j - 3tk and r_2 = {t}^{ 2}i - 2j + tk

    I have found |r_2| = \sqrt{{t}^{ 4} + {t}^{2 } + 4  }

    But now when i differntaite i do not get there answer of

     <br />
\frac{4-{t}^{4}i}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }}  }+ \frac{{t}^{3}+ 8tj}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }} +  \frac{3({t}^{4}-4k}{({t}^{ 4} + {t}^{2 } + 4)^\frac{3}{2 }   }<br />
    Well we can certainly verify that their answer is correct. What is your work? What did you get and how did you get it? We cannot help you unless you tell us what you did.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    Well we can certainly verify that their answer is correct. What is your work? What did you get and how did you get it? We cannot help you unless you tell us what you did.

    -Dan
    Ok so \frac{ti + {t}^{ 2} j - 3tk}{({t}^{4 }+{t}^{2 } +4)^\frac{1}{ 2}   } so first i will just differentiate i \frac{t}{({t}^{4 }+{t}^{2 } +4)^\frac{1}{ 2}  }   } = t({t}^{4 }+{t}^{2 } +4)^\frac{-1}{ 2}   = \frac{-\frac{1}{2 } t({4t}^{3 } +2t)}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}   }
    Last edited by adam_leeds; May 8th 2011 at 11:33 AM.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by adam_leeds View Post
    Ok so \frac{ti + {t}^{ 2} j - 3tk}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}   } so first i will just differentiate i \frac{t}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}  }   } = t({t}^{4 }+{t}^{2 } +4)^\frac{-1}{ 2}   = \frac{-\frac{1}{2 } t({4t}^{3 } +2t)}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}   }
    First, the exponent on the t^4 + t^2 + 4 before you take the derivative is 1/2 not 3/2.

    Your notation is excrescent. Don't simply put equal signs between different steps of a problem.
    \frac{t}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}  }   } = t({t}^{4 }+{t}^{2 } +4)^\frac{-1}{ 2}   = \frac{-\frac{1}{2 } t({4t}^{3 } +2t)}{({t}^{4 }+{t}^{2 } +4)^\frac{3}{ 2}   }

    None of these are equal.

    You wish to find the derivative of
    \frac{t}{(t^4 + t^2 + 4)^{1/2}}

    Use the quotient rule:
    \frac{d}{dt} \left ( \frac{t}{(t^4 + t^2 + 4)^{1/2}} \right ) = \frac{(1)(t^4 + t^2 + 4)^{1/2} - t(1/2)(t^4 + t^2 + 4)^{-1/2}(4t^3 + 2t)}{t^4 + t^2 + 4}

    Now simplify.

    -Dan
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