MHT CET · Maths · Differentiation
If \(\mathrm{y}=\log _3\left(\log _3 x\right)\) then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(x=3\) is \(\ldots \ldots\)
- A \(\frac{1}{3}(\log 3)^{-3}\)
- B \(\frac{1}{3}(\log 3)\)
- C \(\frac{1}{3} \frac{1}{(\log 3)^{-3}}\)
- D \(\frac{1}{3}(\log 3)^{-2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3}(\log 3)^{-2}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{1}{(\log_3 x) \ln 3} \cdot \frac{1}{x \ln 3}\) \(= \frac{1}{x (\log_3 x) (\ln 3)^2}\)
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