| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Implicit or inverse differentiation |
| Difficulty | Moderate -0.3 Part (i) is a straightforward application of the product rule with a standard function. Part (ii) requires implicit differentiation or finding dx/dy then inverting, followed by algebraic manipulation - routine C3 techniques but requires careful execution. Slightly easier than average due to being standard textbook-style exercises. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07q Product and quotient rules: differentiation1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item (i) Differentiate $x ^ { 3 } \ln x$ with respect to $x$.\\
(ii) Given that
\end{enumerate}
$$x = \frac { y + 1 } { 3 - 2 y }$$
find and simplify an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $y$.\\
\hfill \mbox{\textit{OCR C3 Q1 [6]}}