Turunan pertama dari 𝑓(𝑥) = sin3 (5𝑥 + 8) adalah ...
A. 𝑓′ (𝑥) =
3 sin2 (5𝑥 +
8) cos
(5𝑥 + 8)
B. 𝑓′ (𝑥) =
15 sin2 (5𝑥 + 8) cos (5𝑥 + 8)
C.
𝑓′ (𝑥) =
15 cos3 (5𝑥 +
8) cos (5𝑥 +
8)
D.
𝑓′ (𝑥) =
5 cos3 (5𝑥 +
8) cos (5𝑥 +
8)
E. 𝑓′ (𝑥) =
3 cos2 (5𝑥 +
8) cos (5𝑥 +
8)
Jawab:
𝑓(𝑥) =
sin3 (5𝑥 +
8)
𝑓′ (𝑥) =
n · u′ · un – 1
= 3 · 5 cos (5𝑥 +
8) · (sin (5𝑥 +
8))3 – 1
= 15 cos (5𝑥 +
8) sin2 (5𝑥 +
8)
= 15 sin2 (5𝑥 +
8) cos (5𝑥 +
8)
Jawaban : B
Contoh
Turunan pertama dari y =
sin2 (5𝑥 – π) adalah ...
A. y′ (𝑥) =
– 10 sin (5x – π)
B. y′ (𝑥) = – 5 sin (10x – 2π)
C. y′ (𝑥) = – 5 sin (5x – π)
D. y′ (𝑥) = 5 sin (10x – 2π)
E. y′ (𝑥) = 10 sin (10x – 2π)
Jawab:
Ingat identitas
sin 2𝑥 = 2 sin 𝑥 cos 𝑥
y = sin2 (5𝑥 – π)
= (sin (5𝑥 – π))2
y′ (𝑥) = n · u′ · un – 1
= 2 · 5 cos (5𝑥 – π) · (sin (5𝑥 – π))2 – 1
= 5 · 2 cos (5𝑥 – π) · (sin (5𝑥 – π))
= 5 sin (10𝑥 – 2π)
Jawaban : D
Sumber
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