jika f(x)=x2-5x+2/x-4, nilai f'(x)=
Matematika
ValencianaM
Pertanyaan
jika f(x)=x2-5x+2/x-4, nilai f'(x)=
2 Jawaban
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1. Jawaban Jawer17
diangggap gini .... f(x)=(x^2-5x+2)/(x-4)
u = x² - 5x + 2 ... u' = 2x - 5
v = x - 4 ............ v' = 1
f'(x) = (u'v - v'u)/v²
= ((2x - 5)(x - 4) - 1(x² - 5x + 2))/(x - 4)²
= (2x² - 13x + 20 - x² + 5x - 2)/(x - 4)²
= (x² - 8x + 18)/(x - 4)² -
2. Jawaban ArZain
Rumus:
Jika f(x) = u(x)/v(x), maka f'(x) = (u'(x).v(x) - u(x).v'(x))/(v(x))²
Pembahasan:
Misalkan:
u(x) = x² - 5x + 2
u'(x) = 2x - 5
v(x) = x - 4
v'(x) = 1
Maka ↓↓↓
f'(x) = (u'(x).v(x) - u(x).v'(x))/(v(x))²
f'(x) = ((2x - 5)(x - 4) - (x² - 5x + 2)(1))/(x - 4)²
f'(x) = (2x² - 13x + 20 - x² + 5x - 2)/(x² - 8x + 16)
f'(x) = (x² - 8x + 18)/(x² - 8x + 6)