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JAMB Mathematics 1992 Question 37

Question 37

Differentiation

If y = x sin x, find d2y/dx2

  1. A.2cos x − x sin x
  2. B.sin x + x cos x
  3. C.sin x − x cos x
  4. D.x sin x − 2 cos x
Show the answer and explanation

Answer: A (2cos x − x sin x)

Explanation

By the product rule dy/dx = sin x + x cos x. Differentiating again: cos x + cos x − x sin x = 2cos x − x sin x.