Закончит первое задание.
f ' (-1)= 24(4*(-1) +3)^5 = 24*(-1)^5=24*(-1)= - 24.
2) f ' (x)= 2 + 2 sinx;
f '( pi/6) = 2 + 2* sin(pi/6) = 2 + 2*1/2= 2+1= 3.
3) f '(x)=2x/ 2sgrt(x^2-8)= x/sgrt(x^2 - 8);
f '(3) = 3/sgrt(9-8)=3/1=3.
4) f ;(x)=1/2 * 2 * cos 2x=cos 2x;
f '(pi/8) = cos (2*pi/8)= cos(pi/4) = sgrt2/2.
a) f(x)= x^(3/2) -8x^3;
f '(x)= 3/2 x^(1/2) - 24x^2= 3/2* sgrtx -24x^2.
б)f (x)=(3 x^2 -4 +3 - 4/x^4)= 3x^2-1-4x^( -4);
f '(x)=6x +16x^( -5)