Question: Differentiate the following functions with respect to the variable x:

(a)

(b) \[\frac{{{x}^{3}}-3x+1}{{{x}^{3}}+3x+1}\]

(c) \[\frac{1}{{{\left( 1-{{x}^{3}} \right)}^{4}}}\]

(d)

(e) \[\frac{\sin \,3x}{\cos \,3x}\]

(f)