1)y=x^2+3\x+1 2)y=x^2-3x\x-4 Найти производную

Найдем производные функций:

1) y = (x^2 + 3)\(x + 1);  

y  = ((x^2 + 3)\(x + 1)) = ((x^2 + 3) * (x + 1)  - (x + 1) * (x^2 + 3))/(x + 1)^2 = (2 * x * (x + 1) - (x^2 + 3))/(x + 1)^2 = (2 * x^2 + 2 * x - x^2 - 3)/(x + 1) = (x^2 + 2 * x - 3)/(x + 1) = (x + 1)/(x - 3)/(x + 1) = x + 3; 

2) y = (x^2 - 3 * x)\(x - 4); 

y = ((x^2 - 3 * x)\(x - 4)) = ((x^2 - 3 * x) * (x - 4) - (x - 4) * (x^2 - 3 * x))/(x - 4)^2 = ((2 * x - 3) * (x - 4) - (x^2 - 3 * x))/(x - 4)^2 = ( 2 * x^2 - (8 * x - 3 * x + 12 - x^2 + 3 * x)/(x - 4)^2 = (x^2 - 8 * x + 12)/(x - 4)^2 =  (x - 2) * (x - 6)/(x - 4)^2.