Differentiate the function y = csc(x).

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

The function y = csc(x) can be written as y = 1/sin(x). To differentiate this function, we can use the quotient rule. Let u = 1 and v = sin(x), then:

y' = (u'v - v'u)/v^2
y' = (0 - cos(x))/sin^2(x)
y' = -cos(x)/sin^2(x)

Using trigonometric identities, we can rewrite this as:

y' = -1/sin(x) * cos(x)/sin(x)
y' = -csc(x) * cot(x)

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