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WAEC 2023 · Paper 1 · Q30

Differentiate f(x)=1(1−x2)5f(x) = \dfrac{1}{(1 - x^2)^5} with respect to xx.

Worked solution (try it first)
  1. Write it as a power: f(x)=(1−x2)−5f(x) = (1 - x^2)^{-5}.
  2. By the chain rule, f′(x)=−5(1−x2)−6×(−2x)f'(x) = -5(1 - x^2)^{-6} \times (-2x).
  3. The two minus signs make a plus: f′(x)=10x(1−x2)6f'(x) = \dfrac{10x}{(1 - x^2)^6}, option A.

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