6. (i) Given \(x = \tan ^ { 2 } 4 y , 0 < y < \frac { \pi } { 8 }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) as a function of \(x\). Write your answer in the form \(\frac { 1 } { A \left( x ^ { p } + x ^ { q } \right) }\), where \(A , p\) and \(q\) are constants to
be found.
(ii) The volume \(V\) of a cube is increasing at a constant rate of \(2 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\). Find the rate at which the length of the edge of the cube is increasing when the volume of the cube is \(64 \mathrm {~cm} ^ { 3 }\).