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The derivative of y = cot(3x) is -3csc^2(3x).

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

dy/dx = dy/du * du/dx

To find dy/du, we use the derivative of cot(u), which is -csc^2(u). Substituting back in for u, we have:

dy/du = -csc^2(3x)

To find du/dx, we simply take the derivative of u with respect to x, which is 3. Substituting both values back into the chain rule equation, we have:

dy/dx = -csc^2(3x) * 3

Simplifying, we get:

dy/dx = -3csc^2(3x)

Therefore, the derivative of y = cot(3x) is -3csc^2(3x).

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