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Differentiate the function y = tan(2x).

The derivative of y = tan(2x) is 2sec²(2x).

To differentiate y = tan(2x), we will use the chain rule. Let u = 2x, then y = tan(u). Using the chain rule, we have:

dy/du = sec²(u)

du/dx = 2

Therefore, by the chain rule:

dy/dx = dy/du * du/dx
= sec²(u) * 2
= 2sec²(2x)

Hence, the derivative of y = tan(2x) is 2sec²(2x).

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