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Math Help - Differentiation and Integration

  1. #1
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    Differentiation and Integration

    IS it possible to get an answer?


    url=http://www.eyelash.ps/up][/url]
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Maitham
    IS it possible to get an answer?


    url=http://www.eyelash.ps/up][/url]
    Lets do the first derivative problem:

    Differentiate:

    <br />
f(t)=\exp(\mu t + \sigma^2t^2/2)<br />

    Here we need the chain rule:

    <br />
\frac{d}{dt}g(h(t))=\frac{dh}{dt}(t) \times \frac{dg}{dt}(h(t)) <br />
,

    so put h(t)=\mu t + \sigma^2t^2/2 and g(t)=exp(t).

    Then:

    <br />
\frac{d}{dt}f(t)=[\mu+\sigma^2 t][\exp(\mu t + \sigma^2t^2/2)]<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Now lets do the first of the integrals:

    <br />
\int_0^{\infty} \frac{1}{\beta}e^{-x/\beta}dx<br />

    The integrand is the derivative of -e^{-x/\beta} so we know
    (probably from the fundamentaly theorem of calculus) that:

    <br />
\int_0^{\infty} \frac{1}{\beta}e^{-x/\beta}dx=\left[-e^{-x/\beta}\right]_0^{\infty}=-0+1=1<br />

    RonL
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  4. #4
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    Thanks For the answer and i`ll try to do the rest and post the answer to check them for me if they are right, thats if it possible with you.
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