Moderate -0.8 This is a straightforward product rule application with a chain rule component. Students must differentiate x(2x+1)^4, factor out (2x+1)^3, and identify constants by inspection. It's routine calculus with clear structure and no problem-solving insight required—easier than average A-level questions.
3. Given \(y = x ( 2 x + 1 ) ^ { 4 }\), show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x + 1 ) ^ { n } ( A x + B )$$
where \(n , A\) and \(B\) are constants to be found.
3. Given $y = x ( 2 x + 1 ) ^ { 4 }$, show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x + 1 ) ^ { n } ( A x + B )$$
where $n , A$ and $B$ are constants to be found.\\
\hfill \mbox{\textit{Edexcel Paper 2 Q3 [4]}}