: , .
:
. :
1. = ||, 0=0.
2. :
) y = 2 x 5 5 × 2 x + 4 x 7log2 x ln 2;
) y = (1 + x 2) × arctg x;
:
) , :
y' = (2 x 5) ' (5 × 2 x) ' + (4 x) ' (7log2 x) ' (ln 2) ' =
= 2 × (x 5) ' 5 × (2 x) ' + 4 (x) ' 7 × (log2 x) ' 0 =
) , :
y' = (1 + x 2) ' × arctg x + (1 + x 2) ' × (arctg x) ' =
) , :
0=0 , .
3. y = x 2.
4. , S = 6 t 2 + 1, t 1 = 1 t 2 = 3.
1. v (t) = S' (t) t, :
1. (u v) ' = u' v';
2. (Cu) ' = Cu', C = const;
3. C' = 0.
3. (xn) ' = nxn 1.
2. t 1 t 2, .. v (t 1) v (t 2).
3. .
v (t) = S' (t) = (6 t 2 + 1) ' = (6 t 2) ' + 1 ' = 12 t.
v (t 1) = v (1) = 12 1 = 12.
v (t 2) = v (3) = 12 3 = 36.
v. = 23.
5. :
:
) <>
) <>
, (sin2 )' = 2sin x (sin x)' = 2sin x cos x = sin 2 x,
) ,
6. ':
) y + - + = 0;
, ) , ,
ey × y ¢ + e - x (- x)¢ + x ¢ y + xy ¢ = 0
ey × y ¢ - e - x + y + xy ¢ = 0,
, ,
7. , :
.
ln y = 0 Þ y = e 0 = 1. ,
8. 
9. 
10.
11. 
12.
z = ln(1 +x + 2).
1- :
, . :
|
|
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1. , .. : .- 8- ., .- .: , 2007.- 479., . 22.1
2. , .. . : . .- .: , 2012.- 208. 22.1
3. , .. . : . .- .: , 2012.- 416. 22.1
4. .. . . , . 2013. ISBN: 978-5-9061-7227-3
5. .. . . , . 2013. ISBN: 978-5-9061-7228-0
6. .. . . , . 2013. ISBN: 978-5-9061-7230-3
7. .. . . . 2012.
8. .. . . . 2012.
1. : / .. - .: , 2006, 2008, 2009.
2. : . ./ . .. -.:-,2004.
3. ( ): / . .. .: -, 2003.
4. . . . ., , 2004
: .
: , , .
