| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Show derivative equals given algebraic form |
| Difficulty | Moderate -0.3 This is a straightforward application of chain rule in part (i) and product rule in part (ii), with routine algebraic simplification. The 'show that' format removes problem-solving difficulty since the target form is given, making it slightly easier than average but still requiring competent execution of standard differentiation techniques. |
| Spec | 1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
1 (i) Differentiate $\sqrt { 1 + 3 x ^ { 2 } }$.\\
(ii) Hence show that the derivative of $x \sqrt { 1 + 3 x ^ { 2 } }$ is $\frac { 1 + 6 x ^ { 2 } } { \sqrt { 1 + 3 x ^ { 2 } } }$.
\hfill \mbox{\textit{OCR MEI C3 Q1 [7]}}