OCR MEI C3 — Question 5 4 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeShow that derivative equals expression
DifficultyModerate -0.3 Part (i) is a straightforward application of the chain rule to differentiate a simple composite function. Part (ii) requires chain rule with exponential and logarithm, but the working is routine once you recognize the structure. Both are standard C3 differentiation exercises with no problem-solving required, making this slightly easier than average.
Spec1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates

  1. Differentiate \(\sqrt{1 + 2x}\).
  2. Show that the derivative of \(\ln(1 - e^{-x})\) is \(\frac{1}{e^x - 1}\). [4]

\begin{enumerate}[label=(\roman*)]
\item Differentiate $\sqrt{1 + 2x}$.

\item Show that the derivative of $\ln(1 - e^{-x})$ is $\frac{1}{e^x - 1}$. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C3  Q5 [4]}}