tgx=y'
y'=(x²-2)'(x²+2)-(x²-2)(x²+2)' / (x²+2)² = 2x(x²+2)-2x(x²-2)/(x²+2)²=
=2x³+4x-2x³+4x/(x²+2)² = 8x/(x²+2)² = 8*2/(2²+2)²=16/36 =4/9
tgx=4/9
x=arctg 4/9
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y=sin4xcos4x=1/2 sin8x
y'=1/2 *cos8x * 8=4cos8x=4cos 8π/3 = 4cos (2π+2π/3)= - 2 четверть ,cos отриц.
=-4cos π/3 = -4*1/2=-2
tgx=-2
x=-arctg2+πn , n∈Z
Это формулы сокращенного умножения куб суммы и разности
(a+b)^3=((a+b)^2)(a+b)=(a^2+2ab+b^2)(a+b)=a^3+2(a^2)b+ab^2+(a^2)b+2ab^2+b^3=<span>a^3+3a^2b+3ab^2+b^3
</span>(a-b)^3=((a-b)^2)(a-b)=(a^2-2ab+b^2)(a-b)=a^3-2(a^2)b+ab^2-(a^2)b+2ab^2-b^3=<span>a^3-3a^2b+3ab^2-b^3</span>
4*(2^2x) - 5*(2^x) + 1 = 0
2^x = z
4z² - 5z + 1 = 0
D = 25 - 4*4*1 = 9
z₁ = (5 - 3)/8
z₁ = 1/4
z₂ = (5 + 3)/8
z₂ = 1
2^x = 1/4
2^x = 2^(-2)
x₁ = - 2
2^x = 1
2^x = 2^0
x₂ = 0