Soal F(x) = x²+3x+1 x²-2 Tentukan f'(3)?

jawab

turunan

f(x)= (x² + 3x + 1)/(x²-2)

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

y =u/v --> y'  =(u'v - v'u)/(v)²
y' = { (2x+3)(x² -2) - 2x(x² + 3x+1) }/ (x² -2)²
y' = (2x³ -4x+ 3x²- 6 - 2x³ - 6x² -2x ) / (x²-2)²
y' = (5x³- 6x - 5x² - 6) ./ (x² -2)²
f '(3) = ...
x= 3 --> f' (3)  = ( 5.27 - 6.3 - 5.3² - 6) / (3² -2)²
f '(3) = (135- 18- 45- 6) / (9-2)²
f '(3) = (66)/(49)