Y= akar sin x+1/ sin x-1. turunan pertama y adalah?

Turunan
>> TriGonoMetRi

Misal :
u = √(sin x + 1) = (sin x + 1)^1/2
u' = 1/2 (sin x + 1)^-1/2 . cos x
u' = (cos x) / 2√(sin x + 1)

v = sin x - 1
v' = cos x

y = u/v
y' = (u'v - uv')/v²

y'
= (cos x /2√(sin x + 1))(sin x - 1) - √(sin x + 1) . cos x) / (sin x - 1)²
= (1/2 cos x . (sin x - 1) - cos x (sin x + 1)) / ((sin x - 1)² √(sin x + 1))
= (-1/2 cos x sin x - cos x - 1/2) / ((sin x - 1)² √(sin x + 1))
= -1/4 (sin 2x + 4cos x + 2) / ((sin x - 1)² √(sin x + 1))