Let f(x) and g(x) be real valued functions such that f(x)g(x)=1, $\forall x\in R.\text{If }f{}^{\prime \prime }\left(x\right)\text{and}g{}^{\prime \prime }\left(x\right)\text{ exists}\forall x\in R\text{and}{f}^{\prime }\left(x\right)\text{and}{g}^{\prime }\left(x\right)$
are never zero, then prove that $\frac{f{}^{\prime \prime }\left(x\right)}{f^{\prime }\left(x\right)}-\frac{g{}^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}=\frac{2f^{\prime }\left(x\right)}{f\left(x\right)}$

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