This is an example of a function of a function of a function, and we need to apply chain rule 3 times.

Let u = 2x2 and v = csc u.

So y = v2

` (dy)/(dx)`

`=(dy)/(dv)(dv)/(du)(du)/(dx)`

`=[2v][-csc u cot u](4x)`

`=[2 csc(2x^2)]` `xx[(-csc 2x^2)(cot 2x^2)](4x)`

`=-8x(csc^2 2x^2)(cot 2x^2)`

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