| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of quotient |
| Difficulty | Moderate -0.3 This is a straightforward multi-part differentiation question testing standard rules (chain rule for ln, quotient rule, and product rule with exponentials). Each part is routine application of techniques with minimal algebraic manipulation required, making it slightly easier than average for C3 level. |
| 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 |
3. Differentiate each of the following with respect to $x$ and simplify your answers.\\
(i) $\quad \ln ( 3 x - 2 )$\\
(ii) $\frac { 2 x + 1 } { 1 - x }$\\
(iii) $x ^ { \frac { 3 } { 2 } } \mathrm { e } ^ { 2 x }$\\
\hfill \mbox{\textit{OCR C3 Q3 [8]}}