A-LevelMathematicsDifferentiation9709/21 · Oct/Nov 2023 · Q25 Marks
A curve has equation y = 3 tan (1/2)x cos 2x. Find the gradient of the curve at the point for which x = 5/6 π.
- (a)Find the gradient of the curve at the point for which x = 5/6 π.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [B1] State or imply derivative of tan (1/2)x is (1/2) sec² (1/2)x or derivative of cos2x is −2sin 2x
- [*M1] Attempt use of product rule to find first derivative
- [A1] Obtain correct (3/2) sec² (1/2)x cos 2x − 6 tan (1/2)x sin 2x or (unsimplified) equivalent.
- [DM1] Substitute 5/6 π into attempt at first derivative and attempt evaluation to find the gradient
- [A1] Obtain −4
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