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Thread: Help on differentiation

  1. #1
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    Help on differentiation

    $\displaystyle Q(x) = \frac{1}{\sqrt{2 \pi}} \int_x^\infty e^{- t^2/2} dt$

    $\displaystyle P = Q( \sqrt{2a \cdot u^2} ) \cdot e^{au^2}$

    what is the answer if we differentiate P w.r.t. $\displaystyle u^2$ ???

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by graticcio View Post
    $\displaystyle Q(x) = \frac{1}{\sqrt{2 \pi}} \int_x^\infty e^{- t^2/2} dt$

    $\displaystyle P = Q( \sqrt{2a \cdot u^2} ) \cdot e^{au^2}$

    what is the answer if we differentiate P w.r.t. $\displaystyle u^2$ ???

    thanks
    Put $\displaystyle v=u^2$, then:

    $\displaystyle P(v)=Q( \sqrt{2a v} ) ~e^{av}$

    $\displaystyle
    \frac{d}{dv}P(v)=\frac{\sqrt{2a}}{2\sqrt{v}}~Q'(\s qrt{2a v} ) ~ e^{av}+aP(v)
    $

    RonL
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