given-x-y-continuous-and-differenriable-such-that-x-x-t-y-y-t-does-d-2-y-dx-2-d-2-y-dt-2-d-2-x-dt-2-

Question Number 1996 by 123456 last updated on 28/Oct/15

given x, y continuous and differenriable

such that

{\begin{cases} x = x (t) \\ y = y (t) \end{cases}

does

\frac{d^{2} y}{{d x}^{2}} = \frac{\frac{d^{2} y}{{d t}^{2}}}{\frac{d^{2} x}{{d t}^{2}}} ?

Answered by prakash jain last updated on 29/Oct/15

\frac{d y}{d x} = \frac{d y}{d t} \cdot \frac{d t}{d x}

\frac{d^{2} y}{{d x}^{2}} = {(\frac{d t}{d x})}^{2} \cdot \frac{d^{2} y}{{d t}^{2}} + \frac{d y}{d t} \cdot \frac{d^{2} t}{{d x}^{2}}