(cot(x))'

(-csc^2(x)): This term represents negative one times csc^2(x), which is equal to -1/sin^2(x). It describes how fast csc x changes with respect to x.

(-tan^2(x)): This term represents negative one times tan^2(x), which is equal to -1/tan^2x = -cos^2x/sin^2x = -(cosx/sinx)^2. It describes how fast tan x changes with respect to x.

(sec(x) * tan(x)): This term represents the product of sec(x) and tan(x). It describes how fast sec x and tan x change together as x changes.