Given that \(y = ( 4 x + 1 ) ^ { 3 } \sin 2 x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
Given that \(y = \frac { 2 x ^ { 2 } + 3 } { 3 x ^ { 2 } + 4 }\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { p x } { \left( 3 x ^ { 2 } + 4 \right) ^ { 2 } }\), where \(p\) is a constant.
Given that \(y = \ln \left( \frac { 2 x ^ { 2 } + 3 } { 3 x ^ { 2 } + 4 } \right)\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).