Diketahui f(x)=(1+sinx)/(cosx) maka nilai f'(π/6) adalah...

Jawaban yang benar adalah 2 Konsep: • jika f(x) = sin x, maka f'(x) = cos x • jika f(x) = cos x, maka f'(x) = -sin x • jika f(x) = u/v , maka f'(x) = (u'.v - v'.u)/v² • jika x = c, maka f(x) = f(c) • sin 30° = 1/2 • cos 30° = 1/2 √3 Ingat! • π = 180° • (a/b)/(c/d) = a/b x d/c Pembahasan, f(x) = (1 + sin x)/(cos x) Misal, u = 1 + sin x ---> u' = cos x v = cos x ---> v' = -sin x Jadi, f'(x) = (u'.v - v'.u)/v² f'(x) = (cos x. cos x - (-sin x). (1 + sin x))/(cos x)² f'(x) = (cos²x - (-sin x - sin²x))/cos²x f'(x) = (cos²x + sin x + sin²x)/cos²x f'(x) = (sin²x + cos²x + sin x)/cos²x f'(x) = (1 + sin x)/cos²x π/6 = 180°/6 = 30° Jadi, f'(30°) = (1 + sin 30°)/(cos²(30°)) f'(30°) = (1 + 1/2)/(1/2 √3)² f'(30°) = (3/2)/(3/4) f'(30°) = 3/2 x 4/3 f'(30°) = 12/6 f'(30°) = 2 Jadi, f'(π/6) = 2