Kunci Jawaban Matematika Sukino Kelas XII Bab 2 LKS 3 Bag A no 10

Kunci Jawaban Matematika Sukino
Matematika Peminatan Sukino Kelas XII
Bab 2 Turunan Fungsi Trigonometri
LKS 3
Soal dan Pembahasan Matematika Sukino Peminatan
Bagian A

10. Jika h(x) = x² cot x, maka h ' (π/4) sama dengan ...

a. π/8 (4 + π)
b. π/8 (4 - π)
c. π/8 (π - 4)
d. π/4 (8 - π)
e. π/4 (8 + π)

Jawaban : B

h(x) = x² cot x

u = x²
u ' = 2x

v = cot x
v ' = - cosec² x

h ' (x) = 2x . cot x + x² (- cosec² x)
h ' (x) = 2x . cot x - x² cosec² x
h ' (π/4) = 2 . π/4 . cot π/4 - (π/4)² cosec(π/4)²
h ' (π/4) = π/2 . 1 - π²/16 . (2/√2)²
h ' (π/4) = π/2 - π²/16  . 2
h ' (π/4) = π/2 - π²/8
h ' (π/4) = π/8 (4 - π)