Matematika

Pertanyaan

jika f(3-2x)=(1+3x)^4 nilai f'(3)

1 Jawaban

  • f(3 - 2x) = (1 + 3x)⁴

    Misal:
    3 - 2x = a
    x = 3 - a/2

    Maka,
    f(a) = (1 + 3(3 - a/2))⁴
    f(a) = (1 + (9 - 3a/2))⁴
    f(a) = (2 + 9 - 3a/2)⁴
    f(a) = (11 - 3a/2)⁴
    f(x) = (11 - 3x/2)⁴

    f'(x) = (4(-3/2)(11 - 3x/2)³)
    f'(3) = (4(-3/2)(11 - 3(3)/2)³)
    f'(3) = (-6(11 - 9/2)³)
    f'(3) = (-6(2/2)³)
    f'(3) = -6(1) = -6

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