u = 2x + 3
du = 2
v = 3x + 2
dv = 3
y = u/v
y' = (v * du - u * dv) / v^2
y' = ((3x + 2) * 2 - (2x + 3) * 3) / (3x + 2)^2
y' = (6x + 4 - 6x - 9) / (3x + 2)^2
y' = -5 / (3x + 2)^2
(2x + 3) / (3x + 2) =>
(1/3) * (6x + 9) / (3x + 2) =>
(1/3) * (6x + 4 + 5) / (3x + 2) =>
(1/3) * (6x + 4) / (3x + 2) + (1/3) * 5 / (3x + 2) =>
(1/3) * 2 * (3x + 2) / (3x + 2) + 5 / (3 * (3x + 2)) =>
2/3 + 5 / (9x + 6)
u = 9x + 6
u' = 9
2 /3 + 5 * u^(-1)
Derive
0 + 5 * (-1) * u^(-2) * u'
-5 * 9 / (9x + 6)^2 =>
-5 * 9 / (9 * (3x + 2)^2) =>
-5 / (3x + 2)^2
