Calculate the derivative of cot(x).

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

To find the derivative of cot(x), we can use the quotient rule. Recall that cot(x) = cos(x)/sin(x). Therefore,

cot'(x) = [cos'(x)sin(x) - cos(x)sin'(x)]/sin^2(x)

Using the derivatives of sin(x) and cos(x), we get

cot'(x) = [-sin(x)sin(x) - cos(x)cos(x)]/sin^2(x)

Simplifying the numerator, we get

cot'(x) = -[sin^2(x) + cos^2(x)]/sin^2(x)

Recall that sin^2(x) + cos^2(x) = 1, so

cot'(x) = -1/sin^2(x)

Using the identity csc^2(x) = 1/sin^2(x), we can rewrite this as

cot'(x) = -csc^2(x)

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