Differentiate $f ( x ) = \left( \frac { 2 x ^ { 3 } + 1 } { \sqrt [ 3 ] { x } } \right) ^ { 3 }$

Essay

Differentiate $f ( x ) = \left( \frac { 2 x ^ { 3 } + 1 } { \sqrt [ 3 ] { x } } \right) ^ { 3 }$ in three ways: (a) with the chain rule, (b) with the quotient rule but not chain rule, (c) without the chain or quotient rules.