| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Show derivative equals given algebraic form |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question testing standard techniques: chain rule for trigonometric and composite functions in part (a), and quotient rule in part (b). Part (b) requires showing a given result, but the algebra is routine once the quotient rule is applied. All techniques are standard C3 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
2. (a) Differentiate with respect to $x$
\begin{enumerate}[label=(\roman*)]
\item $3 \sin ^ { 2 } x + \sec 2 x$,
\item $\{ x + \ln ( 2 x ) \} ^ { 3 }$.
Given that $y = \frac { 5 x ^ { 2 } - 10 x + 9 } { ( x - 1 ) ^ { 2 } } , x \neq 1$,\\
(b) show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 8 } { ( x - 1 ) ^ { 3 } }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q2 [10]}}