§ 42: 42.1

42.1 Знайдіть другу похідну функції:

1) y’ = 2x – 2; y’’ = 2;

2) y’ = –1x2; y’’ = (–x^–2)’ = 2x^–3 = 2x3;

3) y’ = 12x; y’’ = (2x-12)’ = 2 • (–12)x-12- 1 = –x-32 = –13x2;

4) y’ = –sin x; y’’ = –cos x;

5) y’ = 5(2x – 1)⁴ • 2 = 10(2x – 1)⁴; y’’ = 40(2x – 1)³ • 2 = 80(2x – 1)³;

6) y’ = 2cosx • (–sinx) = –2sinxcosx = –sin2x; y’’ = –2cos2x;

7) y’ = 14cosx4; y’’ = 16 • (sinx4) = –16sinx4;

8) y’ = x’sinx + x(sinx)’ = sinx + xcosx;

y’’ = cosx + cosx – xsinx = 2cosx – xsinx.