Задача 13210 Все на картинке...

u109225536

26.01.2017

Все на картинке

SOVA

26.01.2017

★

1) f`(x)=(x^2)`*(x+2)+(x^2)*(x+2)`=2x*(x+2)+x^2*1=
=3x^2+4x;

2)f`(x)=(x)`*(x+3)^5+(x)*((x+3)^5)`=(x+3)^5+x*5(x+3)^4*(x+3)`=
=(x+3)^4*(x+3+5x)=(x+3)^4*(6x+3);

3)f`(x)=(sqrt(x-1))`*(2x+1)+(sqrt(x-1))*(2x+1)`=
=(2x+1)/2sqrt(x-1)+2sqrt(x-1);

4) f`(x)=(x^4)`*(sqrt(x+1))+(x^4)*(sqrt(x+1))`=4x^3*(sqrt(x+1))+x^4/2sqrt(x-1);

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

6)f`(x)=((x^2-1)`*(2x+1)-(x^2-1)*(2x+1)`)/(2x+1)^2=
=(2x*(2x+1)-(x^2-1)*2)/(2x+1)^2=
=(4x^2+2x-2x^2+2)/(2x+1)^2=
=(2x^2+2x+2)/(2x+1)^2.

7) f`(x)=(x)`*(x+2)^2+(x)*((x+2)^2)`=
=1*(x+2)^2+x*2*(x+2)*(x+2)`=
=1*(x+2)^2+x*2*(x+2)*1=
=(x+2)*(x+2+2x)=(x+2)*(3x+2);

8)f`(x)=((x+1)^2)`*(x-4)^3+((x+1)^2)*((x-4)^3)`=
=2(x+1)*(x-4)^3+(x+1)^2*3*(x-4)^2*(x-4)`=
=(x+1)*(x-4)^2*((2*(x-4)+3(x+1))=(x+1)*(x-4)^2*(5x-5);

9) f`(x)=((sqrt(x+2))`*(3x-1)+(sqrt(x+2))*(3x-1)`=
=(3x-1)/(2sqrt(x+2))+3*sqrt(x+2);

10)f`(x)=(x^3)`*sqrt(x-1)+(x^3)*(sqrt(x-1))`=
=3x^2*sqrt(x-1)+(x^3/(2sqrt(x-1)));

11)f`(x)=((3x-2)`*(x+1)-(3x-2)*(x+1)`)/(x+1)^2=
=(3*(x+1)-(3x-2)*1)/(x+1)^2=
=(3x+3-3x+2)/(x+1)^2=5/(x+1)^2;

12)f`(x)=((x-1)^2)`*(3x-1)-(x-1)^2*(3x-1)`)/(3x-1)^2=
=(2*(x-1)*(3x-1)-(x-1)^2*3)/(3x-1)^2=
=((x-1)*(6x-2-3x+3))/(3x-1)^2=
=((x-1)*(3x+1))/(3x-1)^2.