Question:medium

If \( f(x) = \left(\frac{3+x}{1+x}\right)^{2+3x} \), then \( f'(0) = \)

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For functions of the type \( y = (f(x))^{g(x)} \), use logarithmic differentiation for easier handling.
Updated On: Apr 29, 2026
  • \( 12 + \log 3 \)
  • \( -12 + 3\log 3 \)
  • \( -\frac{4}{3} + 3\log 3 \)
  • \( -12 + 27\log 3 \)
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The Correct Option is D

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