imo class 12 continuity and differentiability

Find the derivative of y = xˣ with respect to x.

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Find the derivative of y = xˣ with respect to x.

  • A. xˣ
  • B. xˣ log x
  • C. xˣ (1 + log x)
  • D. x^(x − 1)

Answer: C) xˣ (1 + log x)

Explanation: Take log on both sides: log y = x log x. Differentiate: (1/y) dy/dx = 1 × log x + x × (1/x) = 1 + log x. dy/dx = y(1 + log x) = xˣ(1 + log x).

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