CUET · MATHS · PYQ PAPER 2025
If \(y=(\log x)^{\log x}, x>1\) then \(\frac{d y}{d x}\) is equal to
- A \(\log x\left[\frac{1+\log (\log x)}{x}\right], x>1\)
- B \((\log x)^{\log x}\left[\frac{1+\log x}{x}\right], x>1\)
- C \((\log x)^{\log x}\left[\frac{x+\log (\log x)}{x}\right], x>1\)
- D \((\log x)^{\log x}\left[\frac{1+\log (\log x)}{x}\right], x>1\)
Answer & Solution
Correct Answer
(D) \((\log x)^{\log x}\left[\frac{1+\log (\log x)}{x}\right], x>1\)
Step-by-step Solution
Detailed explanation
\(\log y = (\log x) \log(\log x)\) \(\frac{1}{y}\frac{dy}{dx} = \left(\frac{1}{x}\right) \log(\log x) + (\log x) \left(\frac{1}{\log x} \cdot \frac{1}{x}\right)\) \(\frac{1}{y}\frac{dy}{dx} = \frac{\log(\log x)}{x} + \frac{1}{x}\)…
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