Найдите производную функции y = (2x+3) ^5

Найдем производную функции у = (2 х + 3) ^5.

у' = 5 * (2 х + 3) ^4 = 5 * (2x + 3) ^2 * (2x + 3) ^2 =

= 5 * ((2x) ^2 + 2 * 2x * 3 + 3^2) ((2x) ^2 + 2 * 2x * 3 + 3^2) =

= 5 * (4x^2 + 12x + 9) (4x^2 + 12x + 9) =

= 5 * (4x^2 * 4x^2 + 4x^2 * 12x + 4x^2 * 9 + 12x * 4x^2 + 12x * 12x + 12x * 9 + 9 * 4x^2 + 9 * 12x + 9 * 9) =

= 5 * (16x^4 + 48x^3 + 36x^2 + 48x^3 + 144x^2 + 108x + 36x^2 + 108x + 81) =

= 5 * (16x^4 + 96x^3 + 216x^2 + 216x + 81) =

= 5 * 16x^4 + 5 * 96x^3 + 5 * 216x^2 + 5 * 216x + 5 * 81 =

= 80x^4 + 480x^3 + 1080x^2 + 1080x + 405.