y = cos(x²), cari d³y/dx³

y = cos x²

dy/dx = - sin x² . 2x = -2x sin x² = u . v
u = -2x => u' = -2
v = sin x² => v' = cos x² . 2x = 2x cos x²

d²y/dx² = u' v + v' u
= -2 sin x² + 2x cos x² . -2x
= -2 sin x² + (-4x²) cos x²
u = -4x² => u' = -8x
v = cos x² => v' = - sin x² . 2x = -2x sin x²

d³y/dx³ = -2 cos x² . 2x + u' v + v' u
= -4x cos x² + (-8x) cos x² + (-2x sin x²) . -4x²
= -12x cos x² + 8x³ sin x²