1.
-8x²-16xy-8y²=-8(x²+2xy+y²)=-8(x+y)²
2.
5mn+15m-10n-30=5m(n+3)-10(n+3)=(n+3)(5m-10)
3.
256-b^4=16²-(b²)²=(16-b²)(16+b²)
Решение смотри в приложении
Производная будет абсолютно такая же как и функция
1) y' = (x)' = 1
2) y'=(-3)' = 0
3) y'=(x^6)' = 6x^(6-1)=6x^5
4) y'=(sqrt(x))' = (x^(1/2))' = 1/2 * x^(1/2-1) = 1/2sqrt(x)
5) y'=(x^(1/3))' = 1/3 * x^(1/3-1) = 1/3 * x^(-2/3)
6) y' = (x^(3/4))' = 3/4 * x^(3/4-1) = 3/4 * x^(-1/4)
7) y' = -sinx
8) y'= 1/(1+x^2)
9) y' = -3*x^(-3-1) = -3*x^(-4) = -3/x^4
10) y' = cosx
11) y' = - 1/(1+x^2)
12) y' = 3^x * ln3
1. а^7*а^2=а^(7+2)=a^9
2. t^9:t^4=t^(9-4)=t^5
3. m^2*m^5=m^(2+5)=m^7
4. c^7:c^2=c^(7-2)=c^5