CAIE P3 2021 November — Question 7 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionNovember
Marks3
TopicImplicit equations and differentiation

7 The equation of a curve is \(\ln ( x + y ) = x - 2 y\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x + y - 1 } { 2 ( x + y ) + 1 }\).
  2. Find the coordinates of the point on the curve where the tangent is parallel to the \(x\)-axis. \(\quad\) [3]