Вячеслав Михайлович
Просветленный
(24801)
1 неделю назад
(x⁴ + 2x³)' = (x⁴)' + (2x³)' = 4x³ + 2 * 3x² = 4x³ + 6x²
(8 cos²(π/2 + x))' = 8 * 2 cos(π/2 + x) * (cos(π/2 + x))'
= 16 cos(π/2 + x) * (-sin(π/2 + x)) * (π/2 + x)'
= 16 cos(π/2 + x) * (-sin(π/2 + x)) * 1
= -16 cos(π/2 + x) sin(π/2 + x)
используя cos(π/2 + x) = -sin(x) и sin(π/2 + x) = cos(x):
= -16 (-sin(x)) (cos(x))
= 16 sin(x) cos(x)
используя sin(2x) = 2 sin(x) cos(x):
= 8 * (2 sin(x) cos(x))
= 8 sin(2x)
альтернативный расчет через упрощение:
8 cos²(π/2 + x) = 8 (-sin(x))² = 8 sin²(x)
(8 sin²(x))' = 8 * 2 sin(x) * (sin(x))'
= 16 sin(x) * cos(x)
= 8 * (2 sin(x) cos(x))
= 8 sin(2x)