| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 8 |
| Topic | Differentiating Transcendental Functions |
| Type | Differentiate logarithmic functions |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing standard rules (chain rule, product rule, quotient rule) with routine simplification. All three parts are textbook exercises requiring direct application of learned techniques without problem-solving or insight, making it easier than average for A-level. |
| 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 |
Find $\frac{dy}{dx}$ for the following functions, simplifying your answers as far as possible.
\begin{enumerate}[label=(\roman*)]
\item $y = \cos x - 2 \sin 2x$ [2]
\item $y = \frac{1}{2}x^4 + 2x^4 \ln x$ [3]
\item $y = \frac{2e^{3x} - 1}{3e^{3x} - 1}$ [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q1 [8]}}