tolong jawab sama bantuin cara nya yaa
Matematika
lisa622
Pertanyaan
tolong jawab sama bantuin cara nya yaa
1 Jawaban
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1. Jawaban arsetpopeye
1) f(x) = sin x / x = u/v
u = sin x => u' = cos x
v = x => v' = 1
f'(x) = (u' v - v' u)/v^2 = (cos x . x - 1 sin x)/x^2 = (x cos x - sin x)/x^2
g(x) = x/(sin x) = u/v
u = x => u' = 1
v = sin x => v' = cos x
g'(x) = (u' v - v' u)/v^2
= (1 sin x - cos x . x)/(sin x)^2
= (sin x - x cos x)/(sin x)^2
= -(x cos x - sin x)/(sin^2 x)
f'(x)/g'(x)
= [(x cos x - sin x)/x^2] / [-(x cos x - sin x)/(sin^2 x)]
= - sin^2 x / x^2
= - ((sin x)/x)^2
2) y = 2x => m = 2
y = x^3 - x^2 + x + 1
y' = 3x^2 - 2x + 1
m = y' => 3x^2 - 2x + 1 = 2
=> 3x^2 - 2x - 1 = 0
=> (3x + 1)(x - 1) = 0
=> x = -1/3 atau x = 1
Xa + Xb = -1/3 + 1 = 2/3