CAIE P3 2016 March — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionMarch
TopicImplicit equations and differentiation

6 A curve has equation $$\sin y \ln x = x - 2 \sin y$$ for \(- \frac { 1 } { 2 } \pi \leqslant y \leqslant \frac { 1 } { 2 } \pi\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
  2. Hence find the exact \(x\)-coordinate of the point on the curve at which the tangent is parallel to the \(x\)-axis.