| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of product |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing product rule and chain rule - both standard C3 techniques. Part (i) is a direct product rule application, and part (ii) is a routine chain rule with a simple power function. No problem-solving or insight required, just mechanical application of learned rules. |
| Spec | 1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
Differentiate each of the following with respect to $x$.
\begin{enumerate}[label=(\roman*)]
\item $x^3(x + 1)^5$ [2]
\item $\sqrt{3x^4 + 1}$ [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q1 [5]}}