The equation of a curve is ln(x+y) = 3x²y. Find the gradient of the curve at the point (1,0).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [B1] State or imply (1/(x+y)) * (1 + dy/dx) as the derivative of ln(x+y)
2. [B1] State or imply 6xy + 3x² dy/dx as the derivative of 3x²y
3. [M1] Substitute (1, 0) and solve for dy/dx Having the correct form for at least one of the above.
4. [A1] Obtain dy/dx = ½ or 0.5
5. Alternative Method for Question 3:
6. [B1] Rewrite as x + y = e^(3x²y) and state or imply 1 + dy/dx as the derivative of the LHS
7. [B1] State or imply (6xy + 3x² dy/dx) e^(3x²y) as the derivative of e^(3x²y)
8. [M1] Substitute (1, 0) and solve for dy/dx Having the correct form for at least one of the above.
9. [A1] Obtain dy/dx = ½ or 0.5