The derivative of a function can be found using the rules of differentiation. For the function \(y = \frac{2x}{\sin x}\), we can use the quotient rule, which states that the derivative of \(\frac{u}{v}\) is \(\frac{vu' - uv'}{v^2}\), where \(u'\) and \(v'\) are the derivatives of \(u\) and \(v\) respectively.

Let \(u = 2x\) and \(v = \sin x\). Then \(u' = 2\) and \(v' = \cos x\).

Substituting these into the quotient rule gives:

\(\frac{\mathrm d y}{\mathrm d x} = \frac{2x \cos x - 2 \sin x}{\sin^2 x} = 2 \csc^2 x - 2x \cot x \csc x\)

Simplifying this gives:

\(\frac{\mathrm d y}{\mathrm d x} = 2 \csc x (1 - x \cot x)\)