Пошаговое объяснение:
1) y = 12x+√x ; y' = ( 12x+√x )' = ( 12x )' + ( √x )' = 12 + 1/(2√x ) ;
2) y = 1/x + 4x ; y' = ( 1/x + 4x )' = ( 1/x )' + ( 4x )' = - 1/x² + 4 ;
3) y = 6√x+3x ; y' = ( 6√x+3x )' = ( 6√x )' + ( 3x )' = 6/2√x+3 = 3/√x+3 ;
4) y = sin x + 3 ; y'= ( sin x + 3 )' = ( sin x )' + 3 ' = cosx + 0 = cosx ;
5) y = cos x + 2x ; y' = ( cos x + 2x )' = ( cos x )' + ( 2x )' = - sin x + 2 .
1) 2 18/31*12,4-2,75:4 5/7= 80/31*124/10-275/100*7/33= 32-1,925/3300= 31 1,375/3300= 31 275/660= 31 55/132
2) 1 2/3 * 3,6 + 2 8/9 : 19,5= 5/3*36/10 + 26/9*10/195= 6+ 100/675= 6 100/675= 6 20/135
= 6 4/27
3) 1 13/55 : 1 1/33 : 0.96 - 0,35= 68/55*33/34 : 0.96-0.35= 66/55*100/96-0.35=220/176-0.35= 1 44/176-0.35= 1 11/44 - 0.35= 1 1/4 - 0.35= 1,25-0.35= 0.9
4) 2 1/22*2 17/30 : 1,3125-3/99= 45/22*77/30:1,3125-3/99= 105/12 * 10000/13125-3/99=6/625000 - 3,99= 6/625000-399/100= 6/625000-2493750/625000= - 2494746/625000= 3.99