| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | October |
| Marks | 8 |
| Topic | Product & Quotient Rules |
| Type | Find derivative of composite quotient/product |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing product rule and quotient rule with standard functions. Both parts are routine applications of A-level differentiation techniques with no problem-solving or insight required—simpler than the typical multi-step calculus question that would score 0.0. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
In all questions you must show all stages of your working, justifying solutions and not relying solely on calculator technology.
(a) Differentiate with respect to $x$
\begin{enumerate}[label=(\roman*)]
\item $x^2 e^{3x + 2}$, [4]
\item $\frac{\cos(2x^4)}{3x}$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q1 [8]}}