Find dy/dx for (4x-5)^3 (4x+2)^3

The easiest way would be this way:

a^c * b^c = (a * b)^c

(4x - 5)^3 * (4x + 2)^3 =>
((4x - 5) * (4x + 2))^3 =>
(16x^2 - 20x + 8x - 10)^3 =>
(16x^2 - 12x - 10)^3

d/du u^n = n * u^(n - 1) * du

u = 16x^2 - 12x - 10
du = 32x - 12

d/dx (16x^2 - 12x - 10)^3 =>
3 * (32x - 12) * (16x^2 - 12x - 10)^2 =>
(96x - 36) * (16x^2 - 12x - 10)^2


Another way would be to use the product rule

d(u * v) = u * dv + v * du

u = (4x - 5)^3
du = 3 * 4 * (4x - 5)^2 => 12 * (4x - 5)^2
v = (4x + 2)^3
dv = 3 * 4 * (4x + 2)^2 => 12 * (4x + 2)^2

udv + vdu =>
(4x - 5)^3 * 12 * (4x + 2)^2 + 12 * (4x - 5)^2 * (4x + 2)^3 =>
12 * (4x - 5)^2 * (4x + 2)^2 * (4x - 5 + 4x + 2) =>
12 * (8x - 3) * ((4x - 5) * (4x + 2))^2 =>
(96x - 36) * (16x^2 - 12x - 10)^2