OCR H240/02 2018 September — Question 1 7 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2018
SessionSeptember
Marks7
TopicProduct & Quotient Rules
TypeFind derivative of quotient
DifficultyModerate -0.8 This is a straightforward differentiation question testing basic quotient rule and chain rule application with standard functions. Part (a) can be done with chain rule alone (rewriting as a power), part (b) is a direct quotient rule application with ln(x+2) and x, and part (ii) is a routine integration by inspection. All are textbook exercises requiring only mechanical application of rules with no problem-solving or insight needed, making it easier than average.
Spec1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)

1
  1. Differentiate the following with respect to \(x\).
    1. \(\frac { 1 } { ( 3 x - 4 ) ^ { 2 } }\)
    2. \(\frac { \ln ( x + 2 ) } { x }\)
    3. Find \(\int \mathrm { e } ^ { ( 2 x + 3 ) } \mathrm { d } x\).

1 (i) Differentiate the following with respect to $x$.
\begin{enumerate}[label=(\alph*)]
\item $\frac { 1 } { ( 3 x - 4 ) ^ { 2 } }$
\item $\frac { \ln ( x + 2 ) } { x }$\\
(ii) Find $\int \mathrm { e } ^ { ( 2 x + 3 ) } \mathrm { d } x$.
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2018 Q1 [7]}}