CAIE P3 2012 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionNovember
TopicParametric equations

3 The parametric equations of a curve are $$x = \frac { 4 t } { 2 t + 3 } , \quad y = 2 \ln ( 2 t + 3 )$$
  1. Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\), simplifying your answer.
  2. Find the gradient of the curve at the point for which \(x = 1\).