The table below shows the values of two functions \(\mathrm p\) and \(\mathrm q\) and their first derivatives when \(x=\sqrt3\), \(x=\dfrac1{\sqrt3}\) and \(x=1\).
| \(x\) | \(\mathrm p(x)\) | \(\mathrm p'(x)\) | \(\mathrm q(x)\) | \(\mathrm q'(x)\) |
|---|---|---|---|---|
| \(\sqrt3\) | 2 | \(\sqrt2\) | 1 | \(\dfrac12\) |
| \(\dfrac1{\sqrt3}\) | 1 | 5 | \(-\pi\) | \(-\sqrt2\) |
| 1 | \(\pi\) | −2 | −1 | 3 |
Find the derivative of the composite function \((\mathrm p\circ\mathrm q)(\cot2x)\) when \(x=\dfrac\pi{12}\).[6]
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