Edexcel C1 — Question 43 5 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks5
PaperDownload PDF ↗
TopicChain Rule
TypeBasic power rule differentiation
DifficultyModerate -0.3 This is a straightforward algebraic manipulation followed by routine differentiation. Part (a) requires expanding and simplifying (standard C1 algebra), while part (b) uses basic power rule on the simplified form. The 'show that' structure removes problem-solving demand, and no chain rule is actually needed if using the hint—slightly easier than average.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.07i Differentiate x^n: for rational n and sums

\(f(x) = \frac{(x^2 - 3)^2}{x^3}, x \neq 0\).
  1. Show that \(f(x) \equiv x - 6x^{-1} + 9x^{-3}\). [2]
  2. Hence, or otherwise, differentiate \(f(x)\) with respect to \(x\). [3]

$f(x) = \frac{(x^2 - 3)^2}{x^3}, x \neq 0$.

\begin{enumerate}[label=(\alph*)]
\item Show that $f(x) \equiv x - 6x^{-1} + 9x^{-3}$. [2]
\item Hence, or otherwise, differentiate $f(x)$ with respect to $x$. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1  Q43 [5]}}