а)y'(x)=(1/2sin2x)'=sin2x
y'(пи/4)=sin пи*2/4=sin пи/2=1
б)y=Vx(3х+3)
a=x(3х+3) a'=3x+3+3x=6x+3
b=Va b'=1/2Va
y'=(6x+3)/2Vx(3х+3)
в)y=x/x^2-2x
y'=(x^2-2x-2x^2+2x)/(x^2-2x)^2=x^2=x(x^3+4x^2-4x^3)=x/(4x^2-3x^3)
г)y=Vx^2+4x
a=x^2+4x a'=2x+4
y'=2(x+2)/2Vx^2+4x=(x+2)/Vx^2+4x
а)y'(x)=(1/2sin2x)'=sin2x
y'(пи/4)=sin пи*2/4=sin пи/2=1
б)y=Vx(3х+3)
a=x(3х+3) a'=3x+3+3x=6x+3
b=Va b'=1/2Va
y'=(6x+3)/2Vx(3х+3)
в)y=x/x^2-2x
y'=(x^2-2x-2x^2+2x)/(x^2-2x)^2=x^2=x(x^3+4x^2-4x^3)=x/(4x^2-3x^3)
г)y=Vx^2+4x
a=x^2+4x a'=2x+4
b=Va b'=1/2Va
y'=2(x+2)/2Vx^2+4x=(x+2)/Vx^2+4x