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WAEC Further Mathematics 2011 Question 14

Question 14

Differentiation

If y2 + xy − x = 0, find dy/dx

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

Answer: C ((1 − y)/(x + 2y))

Explanation

Differentiate implicitly: 2y(dy/dx) + x(dy/dx) + y − 1 = 0, so (2y + x)(dy/dx) = 1 − y and dy/dx = (1 − y)/(x + 2y).