| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Implicit differentiation |
| Difficulty | Moderate -0.3 This is a straightforward application of the chain rule and implicit differentiation with standard functions. Part (i) is routine differentiation of a composite function, and part (ii) applies implicit differentiation to a simple equation then verifies equivalence by substitution—both are textbook exercises requiring no problem-solving insight, making it slightly easier than average. |
| Spec | 1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.07s Parametric and implicit differentiation |
3 (i) Given that $y = \sqrt [ 3 ] { 1 + 3 x ^ { 2 } }$, use the chain rule to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$.\\
(ii) Given that $y ^ { 3 } = 1 + 3 x ^ { 2 }$, use implicit differentiation to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$. Show that this result is equivalent to the result in part (i).
\hfill \mbox{\textit{OCR MEI C3 2010 Q3 [7]}}