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Math Help - Chain rule of second order differential

  1. #1
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    Chain rule of second order differential

    Let x(t)=2t^2+2 and y(t)=3t^4+4t^3, then
    find \frac{d^2y}{dx^2} at point (8,80).

    Thanks.
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  2. #2
    Member sbhatnagar's Avatar
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    Lightbulb Re: Chain rule of second order differential

    To find \frac{d^2y}{dx^2}, you must know y(x).

    x=2t^2+2 \Leftrightarrow t=\pm\sqrt{\frac{x-2}{2}}.

    Therefore,  y=3t^4+4t^3 \Leftrightarrow y=3(\frac{x-2}{2})^2\pm 4(\frac{x-2}{2})^{\frac{3}{2}}

    y(x)=3(\frac{x-2}{2})^2\pm 4(\frac{x-2}{2})^{\frac{3}{2}}

    y'(x)=?

    y''(x)=?
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