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WAEC Further Mathematics 2023 Question 30

Question 30

Differentiation

Differentiate f(x) = 1/(1 − x2)5 with respect to x.

  1. A.10x/(1 − x2)6
  2. B.5x/(1 − x2)6
  3. C.−5x/(1 − x2)6
  4. D.−10x/(1 − x2)6
Show the answer and explanation

Answer: A (10x/(1 − x2)6)

Explanation

f(x) = (1 − x²)⁻⁵, so f′(x) = −5(1 − x²)⁻⁶ × (−2x) = 10x/(1 − x²)⁶.