AQA C3 2013 June — Question 2 6 marks

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
Marks6
PaperDownload PDF ↗
TopicProduct & Quotient Rules
TypeFind derivative of quotient
DifficultyModerate -0.3 Both parts are straightforward applications of standard differentiation rules: (a) product rule with a polynomial and trig function, (b) quotient rule followed by substitution. These are routine C3 exercises requiring only direct application of learned techniques with no problem-solving or insight needed, making them slightly easier than average.
Spec1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates

2
  1. Given that \(y = x ^ { 4 } \tan 2 x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
    (3 marks)
  2. Find the gradient of the curve with equation \(y = \frac { x ^ { 2 } } { x - 1 }\) at the point where \(x = 3\).
    (3 marks)

2
\begin{enumerate}[label=(\alph*)]
\item Given that $y = x ^ { 4 } \tan 2 x$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.\\
(3 marks)
\item Find the gradient of the curve with equation $y = \frac { x ^ { 2 } } { x - 1 }$ at the point where $x = 3$.\\
(3 marks)
\end{enumerate}

\hfill \mbox{\textit{AQA C3 2013 Q2 [6]}}