Jika f'(x) turunan pertama fungsi f(x)=3x^2(1-2x)^5, maka f'(1) adalah

Kelas 11 Matematika
Bab Turunan

^ = pangkat

f(x) = 3x² . (1 - 2x)^5

u = 3x²
u' = 6x

v = (1 - 2x)^5
v' = 5 . (1 - 2x)^4 . (-2)
v' = -10 (1 - 2x)^4

f(x) = 3x² . (1 - 2x)^5
f'(x) = 6x . (1 - 2x)^5 + 3x² . (-10) . (1 - 2x)^4
f'(1) = 6 . 1 . (1 - 2 . 1)^5 + 3 . 1² . (-10) . (1 - 2 . 1)^4
f'(1) = 6 . (-1) - 30 . 1
f'(1) = -6 - 30
f'(1) = -36

f(x) = axⁿ
maka:f'(x) = n.axⁿ⁻¹
fungsi f(x) = 3x² . (1 - 2x)⁻5

u = 3x²
u' = 6x

v = (1 - 2x)⁻5
v' = 5 . (1 - 2x)⁻4 . (-2)
v' = -10 (1 - 2x)⁻4

fungsi f(x) = 3x² . (1 - 2x)⁻5
Maka turunannya :
f(x) = 3x² . (1 - 2x)⁻5
f'(x) = 6x . (1 - 2x)⁻5 + 3x² . (-10) . (1 - 2x)⁻4
f'(1) = 6 . 1 . (1 - 2 . 1)⁻5 + 3 . 1² . (-10) . (1 - 2 . 1)⁻4
f'(1) = -6 - 30
f'(1) = -36

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