| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | March |
| Marks | 10 |
| Topic | Chain Rule |
| Type | Chain rule with single composition |
| Difficulty | Moderate -0.8 This is a straightforward differentiation question testing standard rules (exponential, logarithm, chain rule, quotient rule, and product rule). All parts are routine applications of techniques with no problem-solving required. Part (c) requires the most work with quotient/chain rule combination, but remains mechanical. Easier than average A-level questions which typically require more conceptual understanding or multi-step reasoning. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
Differentiate the following with respect to $x$, simplifying your answers fully
\begin{enumerate}[label=(\alph*)]
\item $y = e^{3x} + \ln 2x$ [1]
\item $y = (5 + x^2)^{\frac{3}{2}}$ [2]
\item $y = \frac{2x}{(5-3x^2)^{\frac{1}{2}}}$ [4]
\item $y = e^{-\frac{3}{x}} \ln(1 + x^3)$ [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2021 Q1 [10]}}