| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Derivative of inverse trig function |
| Difficulty | Standard +0.8 This is a Further Maths question requiring careful application of the chain rule to a composite function involving arctan and a quotient with a square root. While the techniques are standard (chain rule, quotient rule, arctan derivative), the algebraic manipulation to simplify the result is non-trivial and error-prone, making it moderately challenging even for FM students. |
| Spec | 1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
Given that $y = \arctan \frac{x}{\sqrt{1 + x^2}}$
show that $\frac{dy}{dx} = \frac{1}{\sqrt{1 + x^2}}$ [4]
\hfill \mbox{\textit{Edexcel FP3 2014 Q5 [4]}}