A-LevelMathematicsDifferentiation9709/22 · Feb/Mar 2017 · Q46 Marks
Find the gradient of the curve x² sin y + cos 3y = 4 at the point (2, ½π).
- Find the gradient of the curve x² sin y + cos 3y = 4 at the point (2, ½π).[6]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [M1] Use product rule for derivative of x² sin y
- [A1] Obtain 2x sin y + x² cos y dy/dx
- [B1] Obtain –3sin3y dy/dx as derivative of cos 3y
- [A1] Obtain 2xsin y + x² cos y dy/dx – 3sin 3y dy/dx = 0
- [M1] Substitute x = 2, y = ½π to find value of dy/dx (dep occurring at least once)
- [A1] Obtain –⅔ from correct work only
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