Derivative of a Function Represented Parametrically

If the system of equations
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where $f(t)$ and $g(t)$ are differentiable functions and MATH, defines $y$ as a continuous function of $x$ , then the derivative $\frac{dy}{dx}$ of $y$ with respect to $x$ exists and
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The derivatives of higher orders are computed successively:
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and so on.

Example. If $x=a(t-\sin \ t)$, $y=a(1-\cos \ t)$, then
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Example. If MATH, MATH, then
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Example. If $x=e^{-t}$, $y=t^{3}$, then
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MATH

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