nomor 28

Soal 27: * Fungsi: f(x) = 4sin³(2x - 3) * Rumus: Jika f(x) = [g(x)]ⁿ, maka f'(x) = n[g(x)]ⁿ⁻¹ * g'(x) * Penyelesaian: * f'(x) = 3 * 4sin²(2x - 3) * cos(2x - 3) * 2 * f'(x) = 24sin²(2x - 3)cos(2x - 3) Soal 28: * Fungsi: f(x) = cos(x) / (1 + sin(x)) * Rumus: Jika f(x) = u(x) / v(x), maka f'(x) = (u'v - uv') / v² * Penyelesaian: * u = cos(x) => u' = -sin(x) * v = 1 + sin(x) => v' = cos(x) * f'(x) = (-sin(x)(1 + sin(x)) - cos(x)cos(x)) / (1 + sin(x))² * f'(x) = (-sin(x) - sin²(x) - cos²(x)) / (1 + sin(x))² * f'(x) = (-sin(x) - 1) / (1 + sin(x))² * f'(x) = -1 / (1 + sin(x)) * f'(π/4) = -1 / (1 + √2/2) = -2 + √2 Soal 29: * Fungsi: f(x) = x³ * Rumus: Jika f(x) = xⁿ, maka f'(x) = nxⁿ⁻¹ * Penyelesaian: * f'(x) = 3x² * f'(x) > 0 untuk x ≠ 0 * Kurva selalu naik pada seluruh interval bilangan real. Semoga rumus-rumus ini membantu!