Turunan dari f(x) : 3x+4 / 2x+3

Kelas 11 Matematika
Bab Turunan

f(x) = u/v
f'(x) = (u' v - u v')/v²

f(x) = (3x + 4)/(2x + 3)
f'(x) = (3 . (2x + 3) - (3x + 4) . 2)/(2x + 3)²
f'(x) = (6x + 9 - 6x - 8)/(4x² + 12x + 9)
f'(x) = 1/(4x² + 12x + 9)

jawab

f(x) = u/v
f'(x) = u'v - uv' /v²

f(x) = 3x+4 / 2x+3
misal,

u = 3x+4 , u' = 3
v = 2x+3 , v' = 2

f'(x) = u'v - uv' / v²
f'(x) = 3 (2x+3) - (3x+4)(2) / (2x+3)²
f'(x) = 6x + 9 - 6x - 8 / (2x+3)²
f'(x) = 1 / (2x+3)²

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