| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Show dy/dx equals given expression |
| Difficulty | Moderate -0.3 This is a straightforward implicit differentiation question requiring application of the product rule and chain rule to standard terms. It's slightly easier than average because it's a direct 'find dy/dx' question with no additional complications, though it does require careful algebraic manipulation of the resulting expression. |
| Spec | 1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x + 2y^2 + 2x \cdot 2y\frac{dy}{dx} + \frac{dy}{dx} = 0\) | M2 A2 | |
| \(\frac{dy}{dx} = -\frac{2x + 2y^2}{4xy + 1}\) | M1 A1 | (6 marks) |
$2x + 2y^2 + 2x \cdot 2y\frac{dy}{dx} + \frac{dy}{dx} = 0$ | M2 A2 |
$\frac{dy}{dx} = -\frac{2x + 2y^2}{4xy + 1}$ | M1 A1 | (6 marks)\begin{enumerate}
\item A curve has the equation
\end{enumerate}
$$x ^ { 2 } + 2 x y ^ { 2 } + y = 4$$
Find an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.\\
\hfill \mbox{\textit{Edexcel C4 Q1 [6]}}