Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when:
\(y = \left( 2 x ^ { 2 } - 5 x + 1 \right) ^ { 20 }\);
\(y = x \cos x\).
Given that
$$y = \frac { x ^ { 3 } } { x - 2 }$$
show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { k x ^ { 2 } ( x - 3 ) } { ( x - 2 ) ^ { 2 } }$$
where \(k\) is a positive integer.