Differentiation techniques — A/L Combined Mathematics

How do I practise Differentiation techniques?

1 question with a worked solution

1. What is the derivative with respect to x of the function y = x² · sin(x)?
   1. A) 2x cos(x)
   2. B) x² cos(x) - 2x sin(x)
   3. C) 2x sin(x) + x² cos(x)
   4. D) 2x sin(x) - x² cos(x)
   Check my answer

   Correct answer: C) 2x sin(x) + x² cos(x)

   Applying the Product Rule for differentiation d/dx (u · v) = u' v + u v' with u = x² and v = sin(x): dy/dx = (2x) · sin(x) + x² · cos(x) = 2x sin(x) + x² cos(x).

   Show worked solution

   Step 1: Product rule: (uv)' = u'v + uv'. Step 2: u = x² => u' = 2x; v = sin x => v' = cos x. Step 3: dy/dx = 2x sin x + x² cos x. Answer: 2x sin(x) + x² cos(x).
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Differentiation techniques fit in the syllabus?

Year 1 · Term 2