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Differentiate the function y = tan(3x).

The derivative of y = tan(3x) is 3sec²(3x).

To differentiate y = tan(3x), we can use the chain rule. Let u = 3x, then y = tan(u). Using the chain rule, we have:

dy/dx = dy/du * du/dx

To find dy/du, we can use the derivative of tan(u), which is sec²(u). Therefore:

dy/du = sec²(u)

To find du/dx, we can use the derivative of u, which is 3. Therefore:

du/dx = 3

Putting it all together, we have:

dy/dx = dy/du * du/dx
= sec²(u) * 3
= sec²(3x) * 3

Therefore, the derivative of y = tan(3x) is:

dy/dx = 3sec²(3x)

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