Matematika

Pertanyaan

Turunan fungsi f(x) 2xpangkat2-6 per 4x-7 adalah
A. 8xpangkat2-28x-5 per 4x-7
B. (4x-7)pangkat2 per 4(2xpangkat2-5)
C. 4x-5 per 4
D. 8xpangkat2-28x+28 per (4x-7)pangkat2
E. X

2 Jawaban

  • f(x) = (2x² - 6) / (4x - 7)

    u = 2x² - 6 --> u' = 4x
    v = 4x - 7 --> v' = 4

    f'(x) = [u'v - uv'] / v²
    f'(x) = [4x(4x - 7) - (2x² - 6)4] / (4x - 7)²
    f'(x) = [16x² - 28x - 8x² + 24] / (16x² - 56x + 49)
    f'(x) = (8x² - 28x + 24) / (4x - 7)²
  • f(x) = (2x^2 - 6)/(4x - 7)
    u = 2x^2 - 6 => u' = 4x
    v = 4x - 7 => v' = 4
    f'(x) = (u'.v - u.v')/v^2
    f'(x) = [4x(4x -7) - (2x^2 - 6)(4)]/(4x - 7)^2
    f'(x) = [(16x^2 - 28x) - (8x^2 - 24)]/[16x^2 - 56x +49]
    f'(x) = [16x^2 - 28x - 8x^2 + 24]/[16x^2 - 56x + 49]
    f'(x) = [8x^2 - 28x + 24]/[4x - 7]^2

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