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OAU Post-UTME Mathematics 2022 (Batch A) Question 10

Question 10

Differentiation

Differentiate the function y = ln((x + 2)/(x + 3)).

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

Answer: A (1/((x + 2)(x + 3)))

Explanation

y = ln(x + 2) − ln(x + 3), so dy/dx = 1/(x + 2) − 1/(x + 3) = 1/((x + 2)(x + 3)).