Question

KAK TOLONG KERJAKAN SOAL BAGIAN B. INGAT BAGIAN B AJA. SOALNYA GAMPANG. JAWABANYA BELUM TAHU.

Answer 1

Pakai aturan rantai dari luar ke dalam

f'(x) = cos(tan(√sin x)) . sec²(√sin x) . 1/2 sin^(-1/2) x . cos x
misal cos(tan(√sin x)) = t , sec²(√sin x)=u , 1/2 sin^(-1/2) x = v, cos x=w
f"(x) panjang sekali 
f"(x)/f'(x) = t'/t + u'/u + v'/v + w'/w

kita selesaikan satu" aja biar ga panjang

t'/t = -sin(tan(√sin x)) . sec²(√sin x) . 1/2 sin^(-1/2) x . cos x / cos(tan(√sin x)) . sec²(√sin x) . 1/2 sin^(-1/2) x . cos x
= - tan(tan(√sin x)) 

u'/u = 2 sec(√sin x) . sec(√sin x)tan(√sin x) . 1/2 sin^(-1/2) x . cos x/ sec²(√sin x)
=tan(√sin x) sin^(-1/2) x . cos x

v'/v = 1/2 . (-1/2) sin^(-3/2) x / 1/2 sin^(-1/2) x = (-1/2) sin^(-1) x

w'/w = -sin x /  cos x = -tan x

f"(x)/f'(x) = - tan(tan(√sin x)) + tan(√sin x) sin^(-1/2) x . cos x - 1/2 sin^(-1) x -tanx