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Math Help - differentiate

  1. #1
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    Exclamation differentiate

    differentiate




    Differentiate.

    my head is hurting.....please and tyvm <3
    Last edited by mr fantastic; September 27th 2009 at 03:17 AM. Reason: Removed excessive ! and ? in post title.
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  2. #2
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    g(t) = \frac{8t-\sqrt{t}}{t^\frac{1}{3}}

     u = 8t - \sqrt{t}

     v = t^\frac{1}{3}

    u' = 8 - \frac{1}{2}t^\frac{-1}{2}

     v' = \frac{1}{3}t^\frac{-2}{3}

     = \frac{t^\frac{1}{3}.(8- \frac{1}{2}t^\frac{-1}{2}) - (8t - \sqrt{t}).(\frac{1}{3}t^\frac{-2}{3})}{\frac{1}{4}t^\frac{-4}{3}}

     = \frac{8t^\frac{1}{3} - \frac{1}{2}t^\frac{-1}{6} - \frac{8}{3}t^\frac{1}{3} + \frac{1}{3}t^\frac{-1}{6}}{\frac{1}{4}t^\frac{-4}{3}}

    =  \frac{\frac{16}{3}t^\frac{1}{3} - \frac{1}{6}t^\frac{-1}{6}}{\frac{1}{4}t^\frac{-4}{3}}
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  3. #3
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    OH MY...

    v = (5\sqrt{x}+ \frac{6}{5\sqrt[3]{x}})^2

    u = 5\sqrt{x}+ \frac{6}{5\sqrt[3]{x}}

     v = u^2

     \frac{dv}{du} = 2u

     u = 5x^\frac{1}{2} + \frac{6}{5}x^\frac{-1}{3}

     \frac{du}{dx} = \frac{5}{2}x^\frac{-1}{2} -\frac{-6}{15}x^\frac{-4}{3}

     \frac{dv}{dx} = \frac{du}{dx}.\frac{dv}{du}

    = 2u(\frac{5}{2}x^\frac{-1}{2} \frac{-6}{15}x^\frac{-4}{3})

      = \frac{5u}{\sqrt{x}} - \frac{4u}{5\sqrt[3]{x^4}}

      = \frac{5(5\sqrt{x}+ \frac{6}{5\sqrt[3]{x}}) }{\sqrt{x}} - \frac{4(5\sqrt{x}+ \frac{6}{5\sqrt[3]{x}}) }{5\sqrt[3]{x^4}}

     \frac{25\sqrt{x} + \frac{30}{5\sqrt[3]{x}}}{\sqrt{x}} - \frac{20\sqrt{x} + \frac{24}{5\sqrt[3]{x}}}{5\sqrt[3]{x^4}}

    = 25 + \frac{\frac{30}{5\sqrt[3]{5}}}{\sqrt{x}} - \frac{20\sqrt{x}}{5\sqrt[3]{x^4}} + 24

     = 49 + \frac{\frac{30}{5\sqrt[3]{5}}}{\sqrt{x}} - \frac{20\sqrt{x}}{5\sqrt[3]{x^4}}

     = 49 + \frac{\frac{6}{\sqrt[3]{5}}}{\sqrt{x}} - \frac{4\sqrt{x}}{\sqrt[3]{x^4}}
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