| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | October |
| Marks | 5 |
| Topic | Chain Rule |
| Type | Differentiation of logarithmic functions |
| Difficulty | Moderate -0.8 Part (a) is straightforward differentiation of a logarithm using the chain rule (or recognizing ln(3x) = ln(3) + ln(x)). Part (b) requires the quotient rule or product rule with chain rule, then algebraic manipulation to reach the specified form. Both are standard textbook exercises testing routine differentiation techniques with minimal problem-solving required, making this easier than average but not trivial due to the algebraic manipulation in part (b). |
| Spec | 1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$ if $y = 4\ln(3x)$
[2]
\item Differentiate $\frac{2x}{\sqrt{3x+1}}$ giving your answer in the form $\frac{3x+c}{\sqrt{(3x+1)^p}}$,
where $c, p \in \mathbb{N}$
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q2 [5]}}