# Chain rule of second order differential

• November 7th 2011, 12:07 AM
chipai
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.
• November 7th 2011, 02:52 AM
sbhatnagar
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, $y=3t^4+4t^3 \Leftrightarrow y=3(\frac{x-2}{2})^2\pm 4(\frac{x-2}{2})^{\frac{3}{2}}$

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

$y'(x)=?$

$y''(x)=?$