§ 37: 37.5 (1-3)

37.5 Знайдіть похідну функції:

1) y’ = 5'3x-2- 5(3x-2)'(3x-2)2 = 0 • 3x-2- 5 • 3(3x-2)2 = –15(3x-2)2;

2) y’ = x3 • cosx- x3 • (cosx)'cos2x = 3x2cosx+ x3sinxcos2x;

3) y’ = 3-2x2'4+2x- (3- x2)(4+2x)'(4+2x)2 = -2x4+2x- 3- x2 • 2(4+2x)2 = -8x-4x3- 6+2x3(4+2x)2 = -2x2- 8x-6(4+2x)2 = -x3- 4x-32(2+x)2;

4) y’ = x2- 5x'x-7- (x2- 5x)(x-7)'(x-7)2 = 2x-5x-7- x2- 5x • 1(x-7)2 = 2x2- 14x-10x+35- x2+ 5x(x-7)2 = x2- 19x+35(x-7)2.