O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2019 · Q75 Marks
The variables x, y and u are such that y = tan u and x = u³ + 1.
- (i)State the rate of change of y with respect to u.[1]
- (ii)Hence find the rate of change of y with respect to x, giving your answer in terms of x.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] sec² u
- [M1] Attempts dy/dx = dy/du * du/dx or dy/dx = dy/du ÷ dx/du
- [A1] FT their (i) dy/dx = (their sec² u) / (3u²)
- [B1] u = (x-1)^(1/3) soi
- [A1] sec²((x-1)^(1/3)) / (3(x-1)^(2/3)) cao final answer
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