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Math Help - Differentiation

  1. #1
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    Differentiation

    Find the derivative of:



    When t = 2, my calculator says it should be about 36.
    Could you also please show the steps?

    Thanks Guys!
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by iphysics View Post
    Find the derivative of:



    When t = 2, my calculator says it should be about 36.
    Could you also please show the steps?

    Thanks Guys!
    H(t)=9000 \cdot \frac{\ln \left(\frac t4+1\right)}{t^2+25}

    Use the quotient rule : \left(\frac uv\right)'=\frac{u'v-uv'}{v^2}

    Here :
    u(t)=\ln \left(\frac t4+1\right) \implies u'(t)=\frac{\frac 14}{\frac t4+1}=\frac{1}{4 \left(\frac t4+1\right)}

    v(t)=t^2+25 \implies v'(t)=2t


    \begin{aligned} H'(t) &=9000 \cdot \left(\frac{\ln \left(\frac t4+1\right)}{t^2+25}\right)' \\<br />
&=9000 \cdot \frac{\frac{1}{4 \left(\frac t4+1\right)} \cdot (t^2+25)-\ln \left(\frac t4+1\right)\cdot 2t}{(t^2+25)^2} \end{aligned}

    You should be able to continue..
    Last edited by Moo; July 19th 2008 at 05:30 AM.
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