а) f(x)=1/4x^4+7x^3-5x^2+2 b) f(x)=(x^2+5)*(x-3) c) f(x)=(-2x+3)^8

Найдем производные функций:

а) f (x) = 1/4 * x^4 + 7 * x^3 - 5 * x^2 + 2;  

f (x) = (1/4 * x^4 + 7 * x^3 - 5 * x^2 + 2)   = 1/4 * 4 * x^3 + 7 * 3 * x^2 - 5 * 2 * x + 0 = x^3 + 21 * x^2 - 10 * x; 

b) f (x) = (x^2 + 5) * (x - 3);  

f (x) = ((x^2 + 5) * (x - 3)) = (x^2 + 5) * (x - 3) + (x - 3) * (x^2 + 5) = 2 * x * (x - 3) + 1 * (x^2 + 5) = 2 * x^2 - 6 * x + x^2 + 5 = 3 * x^2 - 6 * x + 5;  

c) f (x) = (-2 * x + 3)^8;  

f (x) = ((-2 * x + 3)^8)   = 8 * (-2 * x + 3)^7 * (-2 * x + 3) = 8 * (-2 * x + 3)^7 * (-2 * 1 + 0) = -2 * 8 * (-2 * x + 3)^7 = -16 * (-2 * x + 3)^7.