Al2

Page 1

№ 881.

( (

))′ (x

1) log 2 x3 − x 2 − 1 =

(

2) (log 2 x )

3

3x3 − 2 x 3

)′ = 3 ⋅ (xlogln 2x)

2

2

3) (sin (log 3 x ))′ =

)

− x 2 + 1 ln 2 =

3 ln 2 x x ln 3 2

;

;

cos(log 3 x ) ; 4) (cos 3x)′= –sin 3 x⋅3 x⋅ln 3. x ln 3

№ 882.

y′=(e–x)= –e–x

y′=(ln(–x))′=

график г) у=ψ(x);

−1 1 = −x x

график a) y=f(x);

y′=(sin2x)=2cos 2x график в) y=ϕ(x); y′=(2cos x)′= –2sin x график б) y=g(x).

№ 883.

1) f ′(x)=(2 x+2 –x)′=2 x ln2–2 –xln 2, f ′(x)=0, ln2(2 x–2 –x)=0, ln2 ≠0, 2 x–2 –x=0, 2 x=2 –x ⇒ x= –x, f ′(x)>0 при x>0; f ′(x)<0 при x<0; – +

x=0,

0 x 2) f ′(x)=(3 2x–2xln3)′=2⋅3 2x ln3–2ln 3 f ′(x)=0, ln3(3 2x–1)=0, 2ln3 ≠0, 3 2x–1=0⇒3 2x=1⇒3 2x=30 ⇒ 2x=0, x=0. f ′(x)>0 при x>0; f ′(x)<0 при x<0;

+ 0

x 2 1 1 3) f ′(x)=(x+ln2x)′=1+ =1+ , x>0, f ′(x)=0, 1+ =0 ⇒ x= –1, 2x x x f ′(x)>0

+

при –1

x>0; f ′(x)<0 –

+

0

не существует; x

2 , 2x+1>0 2x + 1 3 2 2x + 3 =0 ⇒ =0 ⇒ х= − f ′(x)=0, 1+ 2x + 1 2x +1 2 1 f ′(x)>0 при x> − ; f ′(x)<0 не существует 2 4) f ′(x)=(x+ln(2x+1))′=1+

38


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Al2 by Robot Max - Issuu