1. y'=9x⁸ 6. (x^1/4)'=1/4x^(-3/4)
y'=4/5*x^(4/5-1) 7. (x^-5/6)'=-5/6x^(-11/6)
2. =4/5x^(-1/5) 8. y'=4(2-5x)³*(-5)
4. y'=-2/3x^(-5/3) 9. y'=-10x⁴
5. x⁻¹⁸'=-18x⁻¹⁹ 10. y'=-4(7x-1)⁻⁵*7
11. [(-3+12x)^1/10]=0.1(-3+12x)^(-0.9)
12. (x/3+2)^(-5/6)'=-5/6(x/3+2)^(-5/6-1)*1/3=-5/6(x/3+2)^(-11/6)*1/3
13. f'(x)=-4x⁻⁵ f'(2)=-4*/32=-1/8
14. f'(x)=1/2(√2-5x) f'(-3)=1/2√17
15. f'(x)=5x⁴ 5x⁴=5 x⁴=1 x=+-1
16. f'(x)=2(1-x) 2(1-x)=(1-x)² x=1 делим на 1-х 2=1-х x=-1
17. f'(x)=2(x-3) 2(x-3)=-3 2x-6=-3 2x=3 x=3/2
18. f'(x)=3(2x-2)² = 4 3(4x²-8x+4)=4 12x²-24x+8=0 3x²-6x+2=0
D=36-24=12 √D=2√3 x1=1/6[6+2√3]=1+√3/3
x2=1-√3/3
19. 8x+4=0 8x=-4 x=-1/2