Buktikan jika f(x) = cosec x maka f'(x) = -cosec x cotan x

Turunan

f(x) = cosec x
f(x) = 1/sin x
u = 1 --> u' = 0
v = sin x --> v' = cos x

f ' (x) =  (u' v - uv' )/(v²)

f' (x) = { 0(sin x) - 1(cos x)} / (sin² x)
f '(x) = {0 - cos x} / (sin² x)
f '(x) = (-cos x / sin x) . (1/sin x)
f '(x) =  - cotan x . cosec x
atau
f '(x) =  - cosec x . cotan x
Terbukti