6)

f(x)=x^3-3x^2 +5x+3
f'(x)=3x^2-6x+5
f'(2)=3*2^2-6*2 + 5 = 12-12+5=5


f(x)=e^x*cosx
f'(x)=e^x*cosx-e^x*sinx
f'(2)= e^2*cos2-e^2*sin2


f(x)= (x^2+2)/(x-3)
f'(x)=(x^2-6x-2)/(x^2-6x+9)
f'(2)=(4-12-2)/(4-12+9) = -10/1=-10




f(x) =x^(1/4)
f'(x)=x^(-3/4)/4
f'(2) = 2^(- 3/4) /4=1/ 2^(11/4)




f(x)= log(6)(9x+4)
f'(x) =9/(9ln6x+4ln6) =9/9ln6 2+4ln6

9)f(x)=x^5

   x0=2

  dx=0.0f(x0+dx)
(2+0.01)^5~32.80804011