3) 3/10
4) 4/14
5) 4/5
6) 4/15
7) 26,3
8) 4,5
9) 19,68
10) 1,6
Объяснение:
3) (6/5-3/4) * 2/3 = ((24-15)/20) * 2/3 = 9/20 * 2/3 = 3/10
4) (8/7-1/14+1/42) * 12/46 = ((48-3+1)/42) * 12/46 = 46/42 * 12/46 = 12/42 = 4/14
5) 1 2/5 + 3/8 - 39/40 = 7/5 + 3/8 - 39/40 = (56 + 15 -39)/40 = 32/40 = 4/5
6) (6/5 - 2/3) * 1/2 = ((18-10)/15) * 1/2 = 8/15 * 1/2 = 4/15
7) 6,8 * 3,5 + 2,5 = 23,8 + 2,5 = 26,3
8) 8,26 - 7,52 : 2 = 8,26 - 3,76 = 4,5
9) 4,6 * 3,9 + 1,74 = 17,94 + 1,74 = 19,68
10) 4,51 - 5,82 : 2 = 4,51 - 2,91 = 1,6
В 4) и 5) дроби сокращены.
Производная произведения
(u*v) ' = u'v + uv'
f ' (x) = (x^2 + 1)' (x^3 - x) + (x^2 + 1)(x^3 - x) ' =
= 2x (x^3 - x) + (3x^2 - 1) (x^2 + 1) =
= 2x^4 - 2x^2 + 3x^4 + 3x^2 - x^2 - 1 =
= 2x^4 - 2x^2 + 3x^4 + 2x^2 - 1 =
= 5x^4 - 1
f ' (1) = 5*1 - 1 = 5 - 1 = 4