Question: Differentiate algebraic and trigonometric functions using the product, quotient and function of a function rules

Differentiate the following functions with respect to the variable x:

1. 
2. \[\frac{{{x}^{3}}-3x+1}{{{x}^{3}}+3x+1}\]
3. \[\frac{1}{{{\left( 1-{{x}^{3}} \right)}^{4}}}\]
4. 
5. \[\frac{\sin \,3x}{\cos \,3x}\]
6. 

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