jika f(x) = sin x/ x dan g(x) = x/sin x , maka f'(x)/g'(x) = ..
Matematika
lintalinarni
Pertanyaan
jika f(x) = sin x/ x dan g(x) = x/sin x , maka f'(x)/g'(x) = ..
2 Jawaban
-
1. Jawaban daffaci
TURUNAN FUNGSI TRIGONOMETRI
Kelas XI Semester 2
f(x) = sin x/x dan g(x) = x/sin x
f'(x) = u'v-uv' / v²
f'(x) = (cos x)(x) - (sin x)(1) / x²
f'(x) = x cos x - sin x / x²
g(x) = x/sin x
g'(x) = u'v-uv' / v²
g'(x) = (1)(sin x) - (x)(cos x) / sin² x
g'(x) = sin x - x cos x / sin² x
f'(x)/g'(x) = (x cos x - sin x)/ x² / (sin x - x cos x)/sin² x
= -(sin x - x cos x) / x² . sin² x / (sin x - x cos x)
= - sin² x / x²
= - (sin x / x)²
Jadi jawabannya adalah - (sin x / x)²
Semoga membantu :) -
2. Jawaban Anonyme
f(x) = sin x / x
f'(x) = [cos x (x) - sin x (1)] / x² = (x cos x - sin x) / x²
g(x) = x / sin x
g'(x) = (1 sin x - x cos x) / (sin² x) = (sin x - x cos x) / (sin² x)
f'(x) / g'(x) = [(x cos x - sin x) / x²] / [(sin x - x cos x) / (sin² x)]
= (x cos x - sin x) (sin² x) / [x² (sin x - x cos x)]
= (x cos x - sin x) (sin² x) / [-x² (x cos x - sin x)]
= -sin² x / x²
= -(sin x / x)²