Да, всё верно
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1) y'=4*(3/2)*x^(3/2-1) +3-2*x^(-2-1)=6x^0,5 +3-2x^(-3)=6/√x -2/(x^3)+3;
3)y'=-3sin3x-2*3cos^2 x *(cosx)'=3sin3x-6cos^2 (-sinx)=3sin(3x)+6sinx cos^2 x
4)y"=(x^(-2/3) +sinx-lnx)'=-2/3 *x^(-2/3 -1) +cosx -1/x=2/3 *x^(-5/3)+cosx -1/x=
=2/3*(1/∛(x^5)+cosx -1/x показатели плохо видно!
1. 1) ctg x = 1; x ∈(- π; 2π).
x = π/4 + πk; k∈<span>Z
x= - 3</span>π/4; π/4; 5<span>π/4.
2) ctgx = - </span>√3; x∈(- π; 2<span>π).
</span>x = - π/6 + 2πk; k ∈Z.
x = - π/6; 5<span>π/6.
</span>
2. 1) ctg x < - 1;x∈(- π; 2π).
- π/4 < x < 0 U 3π/4 < x < 2π U 7π/4 < x < 2<span>π.
</span>2) ctg x ≥ - √3; x ∈ ( - π; 2<span>π).
</span>- π ≤ x ≤ - π/6 U 0 ≤ x ≤5π/6 U π ≤ x ≤ 11 <span>π/6</span>