§ 42: 42.2

42.2 Знайдіть другу похідну функції:

1) y’ = 4x³; y’’ = 12x²;

2) y’ = –5 + 3x²; y’’ = 6x;

3) y’ = –1(x-1)2; y’’ = (–(x– 1)^–2)’ = 2(x-1)3;

4) y’ = (3x)’ = (x13)’ = 13x13-1 = 13x-23; y’’ = –13 • 23x-23-1 = –29x-53 = –293x5;

5) у’ = 3(1 – 3х)² • (–3) = –9(1 – Зх)²;

у’’ = –18(1 – 3х) • (–3) = 54(1 – 3х);

в) y’ = –2sin2x; у’’ = –4cos2х;

7) y’ = 2sinхcosх = sin2х; у’’ = 2cos2х;

8) у’ = х’cosх + x(cos х)’ = cosх – хsinх;

у’’ = –sinх – (sinх + хcosх) = –2sinх – хcosx.