<span>а) y=(3x^2-6x+1)/(2x+1)
у' = ((6x -6)*(2x +1) - (3x</span>² -6x +1)*2)/(2x +1)²<span> =
=(12x</span>²-12x +6x -6 -6x² +12x -2)/(2x +1)² = (6x²+6x -8)/(2x +1)²<span>
b)y=3*3√x -5/x+ 1/x^2 = 9</span>√x -5x^-1 + x^-2
y' = 9/(2√x) + 5x^-2 - 2x^-3 = 9/(2√x) +5/x² - 2/x³
16. 2^(5-10x)>1
log₂2^(5-10x)>log₂1
5-10x>0
x<0,5.
17. 16^x>0,125
2^(4x)>1/8
2^(4x)>1/2³
2^(4x)>2⁻³
4x>-3
x>-3/4.
18. 0,5^x>1/128
0,5^x>(0,5)⁷
x<7.
19. 3^(x+1)<9^(4x²)/√27
3^(x+1)<3^(8x²)/3^(3/2)
3^(x+1)<3^(8x²-3/2)
x+1<8x²-3/2
8x²-x-5/2>0 D=81
x=-0,5 x=0,625
(x+0,5)(x-0,625)>0
-∞_____+_____-0,5_____-_____0,625______+_____+∞
x∈(-∞;-0,5)U(0.625;+∞).
6b-13=-55
6b=-55+13
6b=-42
<span>b=-42/6
b=-7</span>
((а+1)-2а2)((а+1)в квадрате+2а3+2а2+4а4)=(а+1-2а2)(а2+2а+1+2а3+2а2+4а4)=(а+1-2а2)(3а2+2а+1+2а3+4а4)