Question 3 - A-Level Maths

1. Differentiate \(\left( x ^ { 2 } + 1 \right) ^ { \frac { 5 } { 2 } }\) with respect to \(x\).
2. Given that \(y = \mathrm { e } ^ { 2 x } \left( x ^ { 2 } + 1 \right) ^ { \frac { 5 } { 2 } }\), find the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(x = 0\).
A curve has equation \(y = \frac { 4 x - 3 } { x ^ { 2 } + 1 }\). Use the quotient rule to find the \(x\)-coordinates of the stationary points of the curve.
[0pt] [5 marks]
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