§ 37: 37.13

37.13 Знайдіть похідну функції:

1) y’ = 6(3x – 5)⁵ • (3x – 5)’ = 6(3x – 5)² • 3 = 18(3x – 5)⁵;

2) y’ = 3(2x² – 3x + 4)² • (2x² – 3x + 4)’ = 3(2x² – 3x + 4)² • (4x – 3);

3) y’ = (sinx3)’ = cosx3 • (x3)’ = 13 cosx3;

4) y’ = (cos²x)’ = 2cosx • (cosx)’ = –2sinxcos x = –sin2x;

5) y’ = (5tg4x)’ = 5 • 1cos24x • (4x)’ = 20cos24x;

6) y’ = –sin(π4 – x) • (π4 – x) = sin(π4 – x);

7) y’ = (1- x2)’ = 121- x2 • (1 – x²)’ = -2x21- x2 = –x1- x2;

8) y’ = (46x+8)’ = ((6x + 8)14)’ = 14(6x + 8)14-1 • (6x + 8)’ = 64(6x + 8)-34 = 644(6x+8)3;

9) y’ = –3(9x – 2)^–4 • (9x – 2)’ = –27(9x – 2)^–4;

10) y’ = (cosx)’ = 12cosx • (cos x)’ = –sinx2cosx.