diketahui f(x) = sinx - cos x /sin x. jika f' adalah turunan pertama fungsi f, nilai f'(π/3)=... tolong dibantu ya

jawab

sin π/3 = 1/2 √3
cos π/3 = 1/2

turunan  y = u /v
u = sin x - cos x
u'= cos x + sin x

v = sin x
v' = cos x

y = u/v  --> y'   (u' v - uv' )/v²

y' = (cos x +sin x )(sin x)  - (sin x - cos x)(cos x)  / (sin x)²

x = π/3

y' = (cos π/3 + sin π/3 )(sin π/3) - (sin π/3 - cos π/3)(cos π/3) / (sin π/3)²

y' = (1/2 + 1/2 √3)(1/2√3) - (1/2√3 - 1/2)(1/2)  / ( 1/2 √3)²

y' = (1/4 √3 + 3/4) -(1/4√3 - 1/4)   / ( 3/4)

y' = (1/4 √3 + 3/4 - 1/4 √3 + 1/4)  / (3/4)

y' =  (3/4 + 1/4) / (3/4)

y'  =(1) / (3/4)

y' = 4/3