§ 37: 37.12 (1-9)

37.12 Знайдіть похідну функції:

1) y’ = (2x + 3)⁵)’ = 5(2x + 3)⁴ • (2x + 3)’ = 5(2x + 3)⁴ • 2 = 10(2x + 3)⁴;

2) y’ = 18(13x – 6)¹⁷ • (13x – 6)¹⁷ = 18(13x – 6)¹⁷ • 13 = 6(13x – 6)¹⁷;

3) y’ = (cos2x)’ = –sin 2x (2x)’ = –2sin2x;

4) y’ = (sin²x)’ = 2sinx • (sinx)’ = 2sinxcosx = sin2x;

5) y’ = (3ctgx5)’ = 3 • -1sin2x5 • (x5)’ = –3sin2x5 • 15 = –35sin2x5

6) y’ = (2x+1)’ = 122x+1 • (2x + 1)’ = 122x+1 • 2 = 12x+1;

7) y’ (31-x)’ = 13(1 – x)13- 1 • (1 – x)’ = 13(1 – x)-23 • (–1) = –13 • 13(1-x)2;

8) y’ = (x2+ 1)’ = 12x2+ 1 • (x² + 1)’ = 2x2x2+ 1 = xx2+ 1;

9) y’ = (x3- 3x)’ = 12x3- 3x • (x³ – 3x)’ = 3x2- 32x3- 3x;

10) y’ = (14x+5)’ = –1(4x+5)2 • (4x + 5)’ = –4(4x+5)2;

11) y' = –4(6 – 7x)^–5 • (6 – 7x)’ = –4(6 – 7x)^–5 • (–7) = 28(6 – 7x)^–5;

12) y’ = –6(x2x + 4x – 1)^–7 • (x2x + 4x – 1)’ = –6(x2x + 4x – 1)^–7 • (12 • 2x + 4) = –6(x2x + 4x – 1)^–7 • (x + 4);

13) y’ = (sinx)’ = 12sinx • (sin x)’ = cosx2sinx;

14) y’ = (sinx)’ = cosx • (x)’ = cosx2x.