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Given $ \left\{ \begin{align*} x &= f(t)\\ y &= g(t) \end{align*}\right. $

We can compute $\frac{dy}{dx}$ simply by \frac{dy}{dx}=\frac{g'(t)}{f '(t)}

However when I tried to compute $\frac{d^2y}{dx^2}$, I met some problem. I've tried the chain rule but it seemed failed.

Can you please help? Thank you.

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    @robjohn: Ah..I'm very sorry that I forgot to search before asking after a long time not using this site... Thank you for the link.2011-11-07

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Just set y'={dy\over dx}, then {d\over dt} y'={dy'\over dx}{dx\over dt}; whence {d^2y\over dx^2}={ {dy' / dt} \over {dx/dt}}.

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    Thank you for your answer. I just tried to apply '$\frac{d}{dx}$' and did not see that applying '$\frac{d}{dt}$' first then we can solve '$\frac{d}{dx}$' out.2011-11-07