Differentiate (4x+5) / (3x^2+2) ^3

(-60x - 90x + 8) / (3x^2 + 2) ^4 or you could write it as

2 (-30x - 45x + 4) / (3x^2 + 2) ^4

Step-by-step explanation:

Using the Quotient rule:

d (u/v) = (vdu - udv) / v^2

We have:

[3x^2 + 2) ^3 * 4 - (4x + 5) * 3 (3x^2 + 2) ^2 * 6x] / (3x^2 + 2) ^6

= 4 (3x^2 + 2) - 18x (4x + 5) / (3x^2 + 2) ^4

= (12x^2 + 8 - 72x^2 - 90x) / (3x^2 + 2) ^4

= (-60x - 90x + 8) / (3x^2 + 2) ^4

= 2 (-30x - 45x + 4) / (3x^2 + 2) ^4