OCR MEI C3 — Question 1 7 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProduct & Quotient Rules
TypeShow derivative equals given algebraic form
DifficultyModerate -0.3 This is a straightforward application of chain rule in part (i) and product rule in part (ii), with routine algebraic simplification. The 'show that' format removes problem-solving difficulty since the target form is given, making it slightly easier than average but still requiring competent execution of standard differentiation techniques.
Spec1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates

1
  1. Differentiate \(\sqrt { 1 + 3 x ^ { 2 } }\).
  2. Hence show that the derivative of \(x \sqrt { 1 + 3 x ^ { 2 } }\) is \(\frac { 1 + 6 x ^ { 2 } } { \sqrt { 1 + 3 x ^ { 2 } } }\).

1 (i) Differentiate $\sqrt { 1 + 3 x ^ { 2 } }$.\\
(ii) Hence show that the derivative of $x \sqrt { 1 + 3 x ^ { 2 } }$ is $\frac { 1 + 6 x ^ { 2 } } { \sqrt { 1 + 3 x ^ { 2 } } }$.

\hfill \mbox{\textit{OCR MEI C3  Q1 [7]}}