Diketahui f(x) = (2x² + 1)/(2x - 3), x ≠ 3/2. Nilai dari f'(5) =...
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Diketahui f(x) = (2x² + 1)/(2x - 3), x ≠ 3/2. Nilai dari f'(5) =...
1 Jawaban
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1. Jawaban ANIsaRafa
f(x) = (2x² + 1)/(2x - 3)
Misal,
u = 2x² + 1
v = 2x - 3
u' = 4x
v' = 2
f'(x) = u'v - uv'/v²
=> = 4x(2x - 3) - (2x² + 1)(2)/(2x - 3)²
=> = 8x² - 12x - 4x² - 2/(2x - 3)²
=> = 4x² - 12x - 2/(2x - 3)²
f'(5) = 4(5)² - 12(5) - 2/(2(5) - 3)²
=> = 4(25) - 60 - 2/(10 - 3)²
=> = 100 - 60 - 2/7²
=> = 38/49