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WAEC Further Mathematics 2010 Question 12

Question 12

Differentiation

If y = 2(2x + √x)2, find dy/dx

  1. A.2√x(2x + √x)
  2. B.4(2x + √x)(2 + 1/(2√x))
  3. C.4(2x + √x)(2 + √x)
  4. D.8(2x + √x)(2 + √x)
Show the answer and explanation

Answer: B (4(2x + √x)(2 + 1/(2√x)))

Explanation

By the chain rule, dy/dx = 2 × 2(2x + √x) × d/dx(2x + √x) = 4(2x + √x)(2 + 1/(2√x)).