If a curve is represented parametrically by the equation $x=f\left(t\right)\text{and}y=g\left(t\right)\text{ then prove that }\frac{d^{2}y}{{dx}^2}=-{\left[\frac{g^{\prime }\left(t\right)}{f^{\prime }\left(t\right)}\right]}^3\left(\frac{d^{2}x}{{dy}^2}\right)$

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