f(x) = ((3x-1)/(2x+5))³
f(x) = (3x-1)³/(2x+5)³
misal
*(3x-1)³ = u
maka,
u' = (3)(3)(3x-1)² = 9(3x-1)²
*(2x+5)³ = v
v' = (3)(2)(2x+5)² = 6(2x+5)²
f'(x) = (u' v - v' u)/v²
= (9(3x-1)²(2x+5)³ - 6(2x+5)²(3x-1)³)/((2x+5)³)²
= (3(3x-1)²(2x+5)²(3(2x+5)-2(3x-1)))/(2x+5)^6
= (3(3x-1)²(6x+15-6x+2))/(2x+5)⁴
= (3(3x-1)²(17))/(2x+5)⁴
= (51(3x-1)²)/(2x+5)⁴ (D)
Mapel: Matematika
Kelas: 11
Materi: Turunan
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f(x) = ((3x-1)/(2x+5))³
f(x) = (3x-1)³/(2x+5)³
misal
*(3x-1)³ = u
maka,
u' = (3)(3)(3x-1)² = 9(3x-1)²
*(2x+5)³ = v
maka,
v' = (3)(2)(2x+5)² = 6(2x+5)²
f'(x) = (u' v - v' u)/v²
= (9(3x-1)²(2x+5)³ - 6(2x+5)²(3x-1)³)/((2x+5)³)²
= (3(3x-1)²(2x+5)²(3(2x+5)-2(3x-1)))/(2x+5)^6
= (3(3x-1)²(6x+15-6x+2))/(2x+5)⁴
= (3(3x-1)²(17))/(2x+5)⁴
= (51(3x-1)²)/(2x+5)⁴ (D)
Mapel: Matematika
Kelas: 11
Materi: Turunan