turunan pertama dari y= x²cos²x adalah...

Turunan  y = u v

y = x² .cos² x
sederhanakan dulu  cos² x = 1/2 (cos  2x + 1)
y = x² . 1/2 (cos 2x + 1)
y = (1/2 x²) (cos 2x +1)

u = 1/2 x² --> u' = x
v = cos 2x + 1 --> v' = -2 sin 2x

y = u v
y' = u'v + uv'

y' = x( cos 2x + 1) +  (1/2 x²)(-2 sin 2x)
y' = x (cos 2x + 1) -  x² sin 2x
y' = x (2 cos² x) - x² (2 sin x cos x)
y' = 2x cos² x - 2x² sin x cos x
y' = 2x cos x ( cos x - x sin x)