Differentiate the function y = csc(5x).

The derivative of y = csc(5x) is -5csc(5x)cot(5x).

To differentiate y = csc(5x), we can use the chain rule and the derivative of csc(x) which is -csc(x)cot(x). Let u = 5x, then y = csc(u). Using the chain rule, we have:

dy/dx = dy/du * du/dx

dy/du = -csc(u)cot(u) (derivative of csc(u))
du/dx = 5 (derivative of 5x)

Substituting these values, we get:

dy/dx = -csc(5x)cot(5x) * 5
dy/dx = -5csc(5x)cot(5x)

Therefore, the derivative of y = csc(5x) is -5csc(5x)cot(5x).