Edexcel F3 2023 January — Question 1

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2023
SessionJanuary
TopicProduct & Quotient Rules

  1. Given that
$$y = 3 x \arcsin 2 x \quad 0 \leqslant x \leqslant \frac { 1 } { 2 }$$
  1. determine an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
  2. Hence determine the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(x = \frac { 1 } { 4 }\), giving your answer in the form \(a \pi + b\) where \(a\) and \(b\) are fully simplified constants to be found.