A-LevelMathematicsDifferentiation9709/23 · May/June 2022 · Q35 Marks
A curve has equation e2x cos 2y + sin y = 1. Find the exact gradient of the curve at the point (0, 1/6π).
- A curve has equation e2x cos 2y + sin y = 1. Find the exact gradient of the curve at the point (0, 1/6π).[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] Use product rule to differentiate e²ˣ cos 2y. Must be evidence of implicit differentiation
- [A1] Obtain 2e²ˣ cos 2y - 2e²ˣ sin 2y dy/dx
- [B1] Obtain 2e²ˣ cos 2y - 2e²ˣ sin 2y dy/dx + cos y dy/dx = 0
- [M1] Substitute x- and y-values to find value of first derivative. Dependent on at least two terms, with at least one involving dy/dx
- [A1] Obtain 2/√3 or (2√3)/3 or exact equivalent
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