| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of composite quotient/product |
| Difficulty | Easy -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. |
| Spec | 1.07l 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:
\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]}}