1) f(x) = x^3 - 6x + 4;
f '(x) = 3 x^2 - 6;
2) f(x) = x^3 + 2x^2 - 3x + 3;
f '(x) = 3x^2 + 4x - 3;
f '(- 2) = 3*(-2)^2 + 4*(-2) - 3= 12- 8 - 3 = 1;
3) f(x) = 3^x * log3_x;
f '(x) = (3^x) ' * log3_x + 3^x * (log3_x) ' = 3^x * log3_x + 3^x * (1 / x*ln3) =3^x(log3_x + 1 / xln3);
f '( 1) = 3^1 * (log3_1 + 1 / 1*ln3) = 3*(0 + 1/ ln3) =3/ ln3.
4) f(x) = (x^2 - 2) / (x^2 - 4) = (x^2 - 4 + 2) / (x^2 - 4) =
= 1 + 2/(x^2 - 4);
f '(x) = 0 +(2 ' *(x^2 - 4) - 2*(x^2 - 4) ')/(x^2 - 4)^2= (x^2 - 4 - 4x) / (x^2 -4)^2;
f '(3) = (9 - 4 - 12) / (9-4)^2 = - 7 / 25.
4) f(x) = x^(1/10);
f '(x) = 1/10 * x(- 9/10)= x^(-9/10) / 10;
f (5)=5^(- 9/10) / 10 = 1 / 10*5^(9/10)= 1/ 10*корень десятой степени из 5 в девятой степени.