4. (a) Differentiate each of the following with respect to \(x\) and simplify your answers.
- \(\sqrt { 1 - \cos x }\)
- \(x ^ { 3 } \ln x\)
(b) Given that
$$x = \frac { y + 1 } { 3 - 2 y } ,$$
find and simplify an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(y\).