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GUJCET · Maths · Continuity and Differentiability

If \(y = \log_{2026}(\log_{2025}x)\) then \(\frac{d y}{d x}=\) ___________.

  1. A \(\frac{1}{2025x \log x}\)
  2. B \(\frac{1}{x \log x \log 2025}\)
  3. C \(\frac{1}{x \log x \log 2026}\)
  4. D \(\frac{1}{2026x \log x}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{x \log x \log 2026}\)

Step-by-step Solution

Detailed explanation

\(\frac{d y}{d x} = \frac{1}{\log_{2025}x \cdot \ln 2026} \cdot \frac{d}{dx}(\log_{2025}x)\) \(= \frac{1}{\log_{2025}x \cdot \ln 2026} \cdot \frac{1}{x \ln 2025}\)