A-LevelMathematicsDifferentiation9709/21 · Oct/Nov 2019 · Q35 Marks
A curve has equation y = (3 + 2 ln x) / (1 + ln x). Find the exact gradient of the curve at the point for which y = 4.
- (a)A curve has equation y = (3 + 2 ln x) / (1 + ln x). Find the exact gradient of the curve at the point for which y = 4.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [*M1] Use quotient rule (or product rule) to find first derivative Must have correct u and v
- [A1] Obtain (1 / (x(1+ lnx)²)) or (unsimplified) equivalent
- [B1] Use y = 4 to obtain ln x = -2/1 or exact equivalent for x
- [DM1] Substitute for x in their first derivative
- [A1] Obtain -4e^(-2) or exact equivalent Must be simplified to contain a single exponential term
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