Find dy/dx when

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [B1 + B1] - 2 sin 2x and 1/3 cos (x/3) each trig function correctly differentiated
2. [M1] Attempt at product rule
3. [A1ft] cos 2x (1/3 cos(x/3)) - 2 sin 2x sin(x/3) isw ft k₁ sin 2x and k₂ cos(x/3) provided k₁, k₂ are non-zero
4. [B1 + B1] sec² x and 1/x or equivalent with negative indices.
5. [M1] Attempt at quotient rule (with given quotient) or rearrangement to correct product and attempt at product rule
6. [A1] ((sec² x)(1 + ln x) - (tan x)(1/x)) / (1 + ln x)² isw penalise poor bracketing if not recovered