a: y'=3x^2-3*2x+1=3x^2-6x+1

b: y'=1/3*3x^2+1/x^2+1/2*căn x=x^2+1/x^2+1/2*căn x

c: y'=(x-3)'*(x^2+2)+(x-3)*(x^2+2)'

=x^2+2+2x(x-3)=2x^2-6x+x^2+2=3x^2-6x+2

f: y'=10*(2x-5)^9*(2x-5)'=20(2x-5)^9

c: \(\left(x^2+x-3\right)'=2x+1\)

(2x-1)'=2

\(y'=\dfrac{\left(2x+1\right)\cdot\left(2x-1\right)-\left(x^2+x-3\right)\cdot2}{\left(2x-1\right)^2}\)

\(=\dfrac{4x^2-1-2x^2-2x+6}{\left(2x-1\right)^2}=\dfrac{2x^2-2x+5}{\left(2x-1\right)^2}\)

\(f'=\left(2x+1\right)'\cdot\sqrt{2x-x^2}+\left(2x+1\right)\cdot\sqrt{2x-x^2}'\)

\(=2\sqrt{2x-x^2}+\left(2x+1\right)\cdot\dfrac{\left(2x-x^2\right)'}{2\sqrt{2x-x^2}}\)

\(=2\sqrt{2x-x^2}+\left(2x+1\right)\cdot\dfrac{2-2x}{2\sqrt{2x-x^2}}\)

\(=2\sqrt{2x-x^2}+\left(2x+1\right)\cdot\dfrac{1-x}{\sqrt{2x-x^2}}\)

1:

\(\lim\limits_{x\rightarrow-1^-}f\left(x\right)=\lim\limits_{x\rightarrow-1^-}\left(x-1\right)=-1-1=-2\)

\(f\left(-1\right)=-1-1=-2\)

\(\lim\limits_{x\rightarrow-1^+}=-m+2\)

Để hàm số liên tục tại x=-1 thì -m+2=-2

=>-m=-4

=>m=4

a: \(f'\left(x\right)=\dfrac{\left(2x+2\right)'\cdot\left(x-1\right)-\left(2x+2\right)\cdot\left(x-1\right)'}{\left(x-1\right)^2}\)

\(=\dfrac{2\left(x-1\right)-2x-2}{\left(x-1\right)^2}=\dfrac{-4}{\left(x-1\right)^2}\)

y-y0=f'(x0)*(x-x0)

=>y=y0+f'(x0)*(x-x0)=f(x0)+f'(x0)(x-x0)

(d)//-4x+8 nên f(x0)=-4

=>2x+2=-4x+4

=>6x=2

=>x=1/3

f'(1/3)=-4/(1/3-1)^2=-9

y=-4+(-9)(x-1/3)=-4-9x+3=-9x-1

b: (d) vuông góc y=4x+3

=>(d): y=-1/4x+b

(d): y=f(x0)+f'(x0)*(x-x0)

=>f(x0)=-1/4

=>2x+2=-1/4(x-1)=-1/4x+1/4

=>9/4x=-7/4

=>x=-7/9

f'(-7/9)=-4/(-7/9-1)^2=-81/64

y=f(-7/9)+f'(-7/9)*(x+7/9)

=-1/4-81/64(x+7/9)

=-81/64x-79/64

f'(x)=2*3x^2+3*2*(a+2)*x+6a^2

=6x^2+6x(a+2)+6a^2

Δ=(6a+12)^2-4*6*6a^2

=36a^2+144a+144-144a^2

=-108a^2+144a+144

f'(x)>0 với mọi x

=>-108a^2+144a+144<0

=>a<-2/3; a>2

f'(-1)=6

=>6*(-1)^2+6*(-1)*(a+2)+6a^2=6

=>6a^2+6-6a-12=6

=>6a^2-6a-12=0

=>a^2-a-2=0

=>a=2(loại) hoặc a=-1(nhận)