Question

F(x)=x2-3x/x2+2x+1 nilai f'(x) Dan f'(2) adl​

Answer 1

Cara kerja

f(x) = (x² - 3x) / (x² + 2x + 1)

u = x² - 3x

u' = 2x - 3

v = x² + 2x + 1

v' = 2x + 1

f'(x) = (u'v - uv') / v²

= (2x-3)(x²+2x+1) - (x²-3x)(2x+1) / (x²+2x+1)²

= (2x³+x²-4x-3 - (2x³-5x²-3x)) / ((x+1)²)²

= (6x² - x - 3) / (x + 1)^4

f'(2) = (6(2)² - 2 - 3) / (2 + 1)^4

= (24 - 5) / 3^4

= 19/81

Mapel : Matematika

Bab : Turunan fungsi

Kode : 11.2.9

Answer 2

f(x) = (x² - 3x)/x² + 2x + 1

u =x² - 3x, u' = 2x - 3, v = x² +2x + 1, v' = 2x + 2

f'(x) = u/ v, f'(2) = u'v - uv'/v² = 2x - 3(x²+2x+1)- x² - 3x(2x + 2)/x²+2x+1 =2(2)-3(2²)+2(2)+1 -3(2)(2(2)+2/2²+2(2)+1 =4-12+4+1-6+4+2/4+4+1=-3-0/9=-3/9=-1/3