1.
a)y' =2x⁴ - 6 + 3e^(x) = 2x⁴ - 3 + 3e^(x)
2√x √x
б) y' = -2sinx + (1/3)cosx - (1/x)
в) y= ∛(6x+1) -8sin(x/4) = (6x+1)^(1/3) - 8sin(x/4)
y' = (1/3) (6x+1)^(⁻²/₃) * 6 - 8cos(x/4) * (1/4) =
= 2 - 2 cos(x/4)
∛(6x+1)²
г) у=2x² (x-3)=2x³ -6x²
y' = 6x²-12x
2.
f(x) ' =1/2 - sin(x- π/3)
1/2 - sin(x -π/3) =0
sin(x -π/3)=1/2
x- π/3 = (-1)^n * π/6 + πn, n∈Z
x= (-1)^n * π/6 + π/3 + πn, n∈Z
3.
f(x)=x² +2x x₀= -2
f(-2)=(-2)² +2*(-2)=4-4=0
f(x) ' = 2x+2
f(-2) ' = 2*(-2)+2=-4+2= -2
y= 0 + (-2)(x- (-2))= -2(x+2)= -2x-4
y= -2x-4 - уравнение касательной.