| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Basic power rule differentiation |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question requiring simplification of a quotient, then applying the power rule (not actually the chain rule despite the topic label). Part (a) is routine algebra and differentiation; part (b) is a simple verification requiring one more differentiation. Slightly easier than average due to being purely procedural with no problem-solving element, but the algebraic manipulation and second derivative add minor complexity beyond the most basic questions. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(y = \frac{1}{2}x^2 - \frac{3}{4}x^{-2}\) | M1 A1 | |
| \(\frac{dy}{dx} = x + 3x^{-3}\) | M1 A1 | |
| (b) \(\frac{d^2y}{dx^2} = 1 - 9x^{-4} = \frac{x^4 - 9}{x^4}\) | M1 A1 | (6) |
**(a)** $y = \frac{1}{2}x^2 - \frac{3}{4}x^{-2}$ | M1 A1 |
$\frac{dy}{dx} = x + 3x^{-3}$ | M1 A1 |
**(b)** $\frac{d^2y}{dx^2} = 1 - 9x^{-4} = \frac{x^4 - 9}{x^4}$ | M1 A1 | (6)Given that
$$y = \frac{x^4 - 3}{2x^2},$$
\begin{enumerate}[label=(\alph*)]
\item find $\frac{dy}{dx}$, [4]
\item show that $\frac{d^2y}{dx^2} = \frac{x^4 - 9}{x^4}$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q5 [6]}}