Suppose f and g are functions having second derivatives f” and g” everywhere, if f (x) …
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Suppose f and g are functions having second derivatives f” and g” everywhere, if f (x) . g (x) = 1 for all x and f’ and g’ are never zero, then \(\frac{\mathrm{f}^{\prime \prime}(\mathrm{x})}{\mathrm{f}^{\prime}(\mathrm{x})}-\frac{\mathrm{g}^{\prime \prime}(\mathrm{x})}{\mathrm{g}^{\prime}(\mathrm{x})}\) equals
- \(-2 \frac{\mathrm{f}^{\prime}(\mathrm{x})}{\mathrm{f}(\mathrm{x})}\)
- \(-\frac{2 \mathrm{~g}^{\prime}(\mathrm{x})}{\mathrm{g}(\mathrm{x})}\)
- \(-\frac{f^{\prime}(x)}{f(x)}\)
- \(2 \frac{\mathrm{f}^{\prime}(\mathrm{x})}{\mathrm{f}(\mathrm{x})}\)
Answer
(B) - 2 ~g ^ ( x ) g ( x ), (D) 2 f ^ ( x ) f ( x )
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