A-LevelMathematicsDifferentiation9709/33 · May/June 2025 · Q56 Marks
The equation of a curve is xy+y²e^x = 4.
- (a)Show that dy/dx = (y² - yex) / (xex+2y)[4]
- (b)Find the gradients of the tangents to the curve when x = 0.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] State or imply y + x dy/dx as the derivative of xy.
- [B1] State or imply 2ye^x dy/dx + y^2 e^x as the derivative of y^2 e^x.
- [M1] Equate attempted derivative to zero and solve for dy/dx. Need implicit differentiation and attempt at a product.
- [A1] Obtain dy/dx = (-y - y^2 e^x) / (x + 2y e^x) from correct working. AG. Need to see sufficient correct detail.
- [B1] Obtain one correct gradient. E.g. 1/2 at (0,2).
- [B1] Obtain second correct gradient. E.g. -3/2 at (0,-2).
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