imo class 12 continuity and differentiability

If y = logₑ(1 + x + x² + x³), then at x = 0, y′ is:

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If y = logₑ(1 + x + x² + x³), then at x = 0, y′ is:

  • A. 1
  • B. 0
  • C. −1
  • D. 2

Answer: A) 1

Explanation: y = log((1+x)(1+x²)). y′ = 1/(1+x) + 2x/(1+x²). At x=0, y′ = 1 + 0 = 1.

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