Jika f(x)= cos x per sin x+cos x, tentukan f'(pi/4)

jawab

f(x) = (cos x) / (sin x + cos x)
u = sin x
u' = cos x

v = sin x + cos x 
v' = cos x - sin x

v² = (sin x + cos x)² = 1 + sin 2x

y=  u/v
y' = (u' v - u v')/v²

y' = {(cos x)(sinx + cos x)  - sin x(cos x - sin x)} / (1  + sin 2x)
y' = ( sin x cos x + cos² x - sin x cos x + sin² x ) /(1 +sin 2x)
y' =  (cos² x + sin² x) / (1 + sin 2x)
y' = 1/(1 + sin 2x)

f'(π/4) = 1/ (1 + sin 2(π/4))
= 1/(1 + sin π/2)
= 1 /(1 +1)
= 1/ 2