Question

Вторая производная функции одной переменной

Answer 1

y = (2x - 1)⁶

y' = 12(2x-1)⁵

y'' = 120(2x-1)⁴

y''(1) = 120(2-1)⁴ = 120

Ответ: 120

Answer 2

$y=(4x^2-4x+1)^3\\y'=3(4x^2-4x+1)^2(4x^2-4x+1)'\\y'=3(4x^2-4x+1)^2(8x-4)\\y'=(24x-12)(16x^4+16x^2+1-32x^3+8x^2-8x) \\y'=384x^5+576x^3+24x-768x^4-192x^4-288x^2-12+384x^3+96x\\y'=384x^5-960x^4+960x^3-480x^2+120x-12\\y''= 1920x^4-3840x^3+2880x^2-960x+120\\y''(1)=4920-4800=120$

Второй способ 

$y=(4x^2-4x+1)^3\\y'=3(4x^2-4x+1)^2(4x^2-4x+1)'\\ y'=3(4x^2-4x+1)^2(8x-4)\\y'=(4x^2-4x+1)^2(24x-12)\\y''=((4x^2-4x+1)^2)'(24x-12)+(4x^2-4x+1)^2(24x-12)'\\y''=2(4x^2-4x+1)(8x-4)(24x-12)+(4x^2-4x+1)^2*24\\y''=(24x^2-24x+6)(64x^2-64x+16)+24(4x^2-4x+1)^2\\y''(1)=(24-24+6)(64-64+16)+24(4-4+1)^2\\y''(1)=6*16+24=120$