If F(x) = f (x) g (x) and f ’ (x) g ’ (x) = c, then

Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability

1. F’ = c \(\left[\frac{f}{f^{\prime}}+\frac{g}{g^{\prime}}\right]\)
2. \(\frac{\mathrm{F}^{\prime \prime}}{\mathrm{F}}=\frac{f^{\prime \prime}}{f}+\frac{g^{\prime \prime}}{g}+\frac{2 \mathrm{c}}{f g}\)
3. \(\frac{\mathrm{F}^{\prime \prime \prime}}{\mathrm{F}}=\frac{f^{\prime \prime \prime}}{f}+\frac{g^{\prime \prime \prime}}{g}\)
4. \(\frac{\mathrm{F}^{\prime \prime \prime}}{\mathrm{F}^{\prime \prime}}=\frac{f^{\prime \prime \prime}}{f^{\prime \prime}}+\frac{g^{\prime \prime \prime}}{g^{\prime \prime}}\)

Answer

(A) F’ = c [ f f^ + g g^ ], (B) F ^ F = f^ f + g^ g + 2 c f g, (C) F ^ F = f^ f + g^ g

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