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Thread: D(x)

  1. #1
    Member srirahulan's Avatar
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    Exclamation D(x)

    If $\displaystyle y=\frac{x^2}{2}+\frac{x\sqrt{x^2+1}}{2}+\ln{\sqrt{ x+\sqrt{x^2+1}}$ prove this

    $\displaystyle 2y=x\frac{d(y)}{d(x)}+\ln\frac{d(y)}{d(x)}$ In this case i substitute $\displaystyle x=tanx$ but after the solving it become more tough.please help me>>>>>>
    Last edited by srirahulan; Jul 20th 2013 at 09:29 PM.
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  2. #2
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    Re: D(x)

    Have you thought to work out $\displaystyle \displaystyle \begin{align*} \frac{dy}{dx} \end{align*}$?
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  3. #3
    Member srirahulan's Avatar
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    Exclamation Re: D(x)

    $\displaystyle y=\frac{tan^2x}{2}+\frac{secxtanx}{2}+\ln[\sqrt{secx+tanx}] \\ \frac{d(y)}{dx}=sec^2xtanx+\frac{sec^3x+secxtanx}{ 2}+\frac{secx(secx+tanx)}{2(secx+tanx)}$



    after that I cannot arrange what ther ask>>>>>>
    Last edited by srirahulan; Jul 20th 2013 at 11:22 PM.
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  4. #4
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    Re: D(x)

    I don't know why you're substituting tan(x), or ANY other function for that matter. Just take the derivative...
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