Question Number 1996 by 123456 last updated on 28/Oct/15
$$\mathrm{given}\:{x},{y}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{differenriable} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\begin{cases}{{x}={x}\left({t}\right)}\\{{y}={y}\left({t}\right)}\end{cases} \\ $$$$\mathrm{does} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }}{\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }}? \\ $$
Answered by prakash jain last updated on 29/Oct/15
$$\frac{{dy}}{{dx}}=\frac{{dy}}{{dt}}\centerdot\frac{{dt}}{{dx}} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\left(\frac{{dt}}{{dx}}\right)^{\mathrm{2}} \centerdot\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }+\frac{{dy}}{{dt}}\centerdot\frac{{d}^{\mathrm{2}} {t}}{{dx}^{\mathrm{2}} } \\ $$