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UI Post-UTME Mathematics 2024 (Model questions) Question 8

Question 8

Differentiation

If y = e2x sin x, find dy/dx

  1. A.e2x cos x
  2. B.2e2x sin x
  3. C.ex cos x
  4. D.e2x(2 sin x + cos x)
Show the answer and explanation

Answer: D (e2x(2 sin x + cos x))

Explanation

Product rule: dy/dx = 2e²ˣ sin x + e²ˣ cos x = e²ˣ(2 sin x + cos x).