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A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2024 · Q36 Marks

A curve has equation 6e⁻ˣy² + e²ˣ – 12y + 7 = 0. Find the gradient of the curve at the point (ln 3, 2).

  1. Find the gradient of the curve at the point (ln 3, 2).[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1] Use product rule to differentiate 6e⁻ˣy²
  2. [A1] Obtain -6e⁻ˣy² + 12e⁻ˣy (dy/dx)
  3. [B1] Obtain +2e²ˣ – 12 (dy/dx)
  4. [M1] Rearrange correctly to obtain dy/dx = ...
  5. [M1] Substitute for x and y to obtain an exact final answer
  6. [A1] Obtain 5/2 or 2.5

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 2, question 3.

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