imo class 12 continuity and differentiability

If y = x² eˣ, what is dy/dx?

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If y = x² eˣ, what is dy/dx?

  • A. 2x eˣ
  • B. x eˣ (x + 2)
  • C. x² eˣ
  • D. eˣ (x² + 1)

Answer: B) x eˣ (x + 2)

Explanation: Using the product rule: u'v + uv' = (2x)(eˣ) + (x²)(eˣ) = x eˣ (2 + x).

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