O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2013 · Q78 Marks
Differentiate, with respect to x,
- (i)(3-5x)¹²,[2]
- (ii)x² sin x,[2]
- (iii)tan x / (1 + e^(2x))[4]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [M1] (i) k(3-5x)¹¹
- [A1] (i) -60(3 - 5x)¹¹ or better, isw
- [M1] (ii) x²(their cos x) + (their 2x) sin x
- [A1] (ii) x² cos x + 2x sin x isw
- [B1] (iii) d(tan x)/dx = sec² x
- [B1] (iii) d(1+e^(2x))/dx = 2e^(2x)
- [M1] (iii) ( (1+e^(2x))(their sec² x) – (their 2e^(2x))tan x ) / (1+e^(2x))²
- [A1] (iii) ( (1+e^(2x)) sec² x - 2e^(2x) tan x ) / (1+e^(2x))² isw
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