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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2019 · Q14 Marks

Given that y = sinx / lnx², find an expression for dy/dx.

  1. Given that y = sinx / lnx², find an expression for dy/dx.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] Either: Quotient rule: d/dx(sinx) = cosx soi
  2. [B1] d/dx(lnx²) = 2/x oe soi
  3. [M1] (lnx²) (their cosx)-(sinx) (their 2/x) / (lnx²)² oe
  4. [A1] (lnx)² cosx-(sinx)(2/x) / (lnx²)² oe isw
  5. [B1] Or: Product rule on y = (sinx)(lnx²)⁻¹ d/dx(sinx) = cosx soi
  6. [B1] d/dx((lnx²)⁻¹) = -(lnx²)⁻² x 2/x
  7. [M1] (sinx) x their (-(lnx²)⁻² x 2/x) + (their cosx)(lnx²)⁻¹ oe
  8. [A1] (sinx)x(-(lnx²)⁻²x 2/x) + (cosx)(lnx²)⁻¹ oe isw

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2019 Paper 2 Variant 2, question 1.

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