If \( y=\frac{u}{v} \), where \( u \& v \) are functions of ' \( x \) ', show that, \( v^{3} \fr...

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If \( y=\frac{u}{v} \), where \( u \& v \) are functions of ' \( x \) ', show that, \( v^{3} \frac{d^{2} y}{d x^{2}}=\left|\begin{array}{ccc}u & v & 0 \\ u^{\prime} & v^{\prime} & v \\ u^{\prime \prime} & v^{\prime \prime} & 2 v^{\prime}\end{array}\right| \).
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