OCR C3 2010 June — Question 1 6 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2010
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProduct & Quotient Rules
TypeFind derivative of composite quotient/product
DifficultyEasy -1.2 This is a straightforward differentiation question testing three standard techniques (product rule, chain rule, quotient rule) with simple functions. Each part is routine application of a single rule with no problem-solving required, making it easier than average for A-level. The 2-mark allocation per part confirms these are basic exercises.
Spec1.07l Derivative of ln(x): and related functions1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates

Find \(\frac{dy}{dx}\) in each of the following cases:
  1. \(y = x^3 e^{2x}\), [2]
  2. \(y = \ln(3 + 2x^2)\), [2]
  3. \(y = \frac{x}{2x + 1}\). [2]

Find $\frac{dy}{dx}$ in each of the following cases:
\begin{enumerate}[label=(\roman*)]
\item $y = x^3 e^{2x}$, [2]
\item $y = \ln(3 + 2x^2)$, [2]
\item $y = \frac{x}{2x + 1}$. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR C3 2010 Q1 [6]}}