1) a) 6x-3x² б)8x+6 в)(9x⁴-1)'=36x³ г) ((1+x²)-x*2x)/(1+x²)²=(1-x²)/(1+x²)²
2) y'=-18x² y'(8)=-1152
3) f(x)=x²-2x x₀=-2
f(-2)=4+4=8 f'(x)=2x-2 f'(-2)=-4-2=-6
y=8+6(x+2) y=6x+20
4) S(t)=2,5t²+1,5t t₀=4
V(t)=S'(t)=5t+1,5 V(4)=20+1,5=21,5
5) f'(x)=((x²+3)-x*2x)/(x²+3)²=(3-x²)/(x²+3)²
(x²+3)²>0⇒(3-x²)>0 (√3-x)(√3+x)>0 (-√3;√3)