FP2

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  1. nazgul60's Avatar
    1 22-06-2012  00:40
    • Full Member
    • Posts: 128
    FP2
    Click image for larger version.  Name: Untitled.png  Views: 64  Size: 23.5 KB  ID: 159200

    Can someone talk me through this part of the question which i dont get.

    Thanks
  2. Siddhu33's Avatar
    2 22-06-2012  00:51
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    • Posts: 10
    Re: FP2
    Product rule:

    E^x(2y*y' + y^2 + 1 + 2*([y]'y' + y*y'') + 2yy')

    E^x(2y*y'' + 2(y')^2 + 4y*y' + y^2 + 1)
  3. SecondHand's Avatar
    3 22-06-2012  00:57
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    Re: FP2
    Differentiate the function with the product rule. Gonna work my latex on this one..

    \displaystyle \frac{d^2y}{dx^2}= e^x\left(2y\frac{dy}{dx}+y^2+1 \right)

    v=e^x
    u=2y\frac{dy}{dx}+y^2+1
    v'=e^x
    u'=2y\frac{d^2y}{dx^2}+ 2\left(\frac{dy}{dx} \right)^2+2y\frac{dy}{dx}

    \displaystyle \frac{d^3y}{dx^3}=vu'+uv'
    \displaystyle \frac{d^3y}{dx^3}=e^x \left(2 \left(\frac{dy}{dx} \right)^2+2y\frac{dy}{dx} \right) + e^x \left(2y\frac{d^2y}{dx^2}+ 2y\frac{dy}{dx}+y^2+1 \right)

    \displaystyle \frac{d^3y}{dx^3}=e^x \left(2y\frac{d^2y}{dx^2}+ 2 \left(\frac{dy}{dx} \right)^2+4y\frac{dy}{dx} +y^2+1 \right)

    If your exam's tomorrow then goodluck
    Last edited by SecondHand; 22-06-2012 at 01:28. Reason: error differentiating
  4. RVNmax's Avatar
    4 22-06-2012  01:23
    • Adored and Respected Member
    Re: FP2
    (Original post by SecondHand)
    Differentiate the function with the product rule. Gonna work my latex on this one..

    \displaystyle \frac{d^2y}{dx^2}= e^x\left(2y\frac{dy}{dx}+y^2+1 \right)

    v=e^x
    u=2y\frac{dy}{dx}+y^2+1
    v'=e^x
    u'=2\left(\frac{dy}{dx} \right)^2+2y\frac{dy}{dx}

    \displaystyle \frac{d^3y}{dx^3}=vu'+uv'
    \displaystyle \frac{d^3y}{dx^3}=e^x \left(2 \left(\frac{dy}{dx} \right)^2+2y\frac{dy}{dx} \right) + e^x \left( 2y\frac{dy}{dx}+y^2+1 \right)

    \displaystyle \frac{d^3y}{dx^3}=e^x \left(2 \left(\frac{dy}{dx} \right)^2+4y\frac{dy}{dx} +y^2+1 \right)

    If your exam's tomorrow then goodluck

    You missed out the 1st term within the brackets in the answer due to an error in differentiating 'u' in line 5
  5. SecondHand's Avatar
    5 22-06-2012  01:26
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    Re: FP2
    (Original post by RVNmax)
    You missed out the 1st term within the brackets in the answer due to an error in differentiating 'u' in line 5
    So I did, thanks for that one. Fixed now, why I am doing maths at 1:30am (
    Last edited by SecondHand; 22-06-2012 at 01:28.
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