Question 2 - A-Level Maths

Exam Board	OCR
Module	FP2 (Further Pure Mathematics 2)
Year	2006
Session	June
Topic	Integration using inverse trig and hyperbolic functions

Given that $y = \tan ^ { - 1 } x$, prove that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 1 + x ^ { 2 } }$.
Verify that $y = \tan ^ { - 1 } x$ satisfies the equation $$\left( 1 + x ^ { 2 } \right) \frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 2 x \frac { \mathrm {~d} y } { \mathrm {~d} x } = 0$$