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WAEC Further Mathematics 2024 Question 31

Question 31

Differentiation

If y2 + 2xy − 8 = 0, find dy/dx

  1. A.dy/dx = (2y + x)/y
  2. B.dy/dx = (2y − x)/(−y)
  3. C.dy/dx = −y/(y + x)
  4. D.dy/dx = y/(2y − x)
Show the answer and explanation

Answer: C (dy/dx = −y/(y + x))

Explanation

Differentiate implicitly: 2y dy/dx + 2y + 2x dy/dx = 0, so dy/dx(2y + 2x) = −2y and dy/dx = −y/(x + y).