Matematika

Pertanyaan

jika f(×)=(2x-1)^2(x+2),maka turunanya f(x)=...

2 Jawaban

  • y = u.v => y' = u'v + uv'
    u = (2x-1)² ; v = x+2
    f'(x) = 2(2x-1).2.(x+2) + (2x-1)².1
           = 4(2x²+4x-x-2) + (4x²-4x+1)
           = 8x² + 12x - 8 + 4x² - 4x + 1
           = 12x² + 8x - 7
  • f(x) = (2x - 1)² (x + 2)

    f '(x)
    = (2x - 1)² . 1 + 2 . 2(2x - 1) . (x + 2)
    = (2x - 1)² + 4(2x - 1)(x + 2)
    = 4x² - 4x + 1 + 4(2x² + 4x - x - 2)
    = 4x² - 4x + 1 + 4(2x² + 3x - 2)
    = 4x² - 4x + 1 + 8x² + 12x - 8
    = 12x² + 8x - 7

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