Matematika

Pertanyaan

tolong carikan turunan dari fungsi berikut

1. f(x) = x + 1/x =

2. f(x) = x² + 1/√x =

3. f(x) = √x (x³-x) =

2 Jawaban

  • 1. f'(x) = 1 + (-1/ akar x)
    2. 
    f'(x) = 2x + (-1/2 x pangkat -1) =
    3. f'(x) = 3/2x pangkat 1/2 - 1/2 x pangkat  - 1/2 =
  • Turunan

    1. f(x)= x + 1/x --> f(x)= x + x⁻¹
    f ' (x) = 1 - 1 x⁻² = 1 - 1/x² = (x²-1)/(x²)

    2. f(x)= x² + 1/√x = x² + x⁻¹/²
    f ' (x)=  2x - 1/2 x⁻³/²
    f ' (x)= 2x - 1/(2x³/²)
    f '(x)= 2x - 1/(2 x√x) = (4x³ - √x)/ (2x²)

    3. f(x)= √x (x³ - x) = x³√x - x√x = x⁷/² - x³/²
    f '(x)= 7/2 x⁵/² - 3/2  x¹/²
    f '(x)= 7/2 x²√x - 3/2 x√x
    f '(x)= (7/2 x² -3/2 x) √x

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