For x>1 , if (2 x)^ 2 y =4 e^ 2 x-2 y , then (1+ _ e 2 x )^ 2 d y d x is equal to:
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
For \(x>1\), if \((2 x)^{2 y}=4 e^{2 x-2 y}\), then \(\left(1+\log _{\mathrm{e}} 2 x\right)^{2} \frac{d y}{d x}\) is equal to:
- \(\frac{x \log _{\mathrm{e}} 2 \mathrm{x}-\log _{\mathrm{e}} 2}{x}\)
- \(\log 2 x\)
- \(x \log _{x} 2 x\)
- \(\frac{x \log _{\mathrm{e}} 2 x+\log _{\mathrm{e}} 2}{x}\)
Answer
(A) x _ e 2 x - _ e 2 x
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