2. (a) Given that \(y = x \arcsin x , 0 \leqslant x \leqslant 1\), find
- an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
- the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(x = \frac { 1 } { 2 }\).
(b) Given that \(y = \arctan \left( 3 \mathrm { e } ^ { 2 x } \right)\), show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 3 } { 5 \cosh 2 x + 4 \sinh 2 x }$$