Odpovědi na početní cvičení
149 ,
I.--r-----7 2. 2X — d — O
Xz
I.
g\x)
1
COS2 X
X3 X4
are tg:
fg-gf
.2 I — COS 2X
3. sin x = -
4.---\Jx2
2 3
3 1
5.1—Vx1--—     ó.xarctgx    7.2(x+2)(x+3)2(3X2+nx+9)    8.ex(2xsinx+x2 cosx+x2 sinx)
2
r
=   I + tg X
2.
4-X
ln2 x + ln x + 1
2X
'i + x'
(1 -x)í? ^d + fc + ^-^x]
(x2 + i)2      5* (lnx+1)2
3(x2 + i)V 1 — x
(i + x)
1.
b+i 1
2v^
i. — tg X      2. 2X ln
i+x2       > .r+eA I + X
I — X
" x ln x ln(ln x)
4.x sin x
1 + cos x
9. e
7.- i      8. (are sin x)2
(X2 — 2)V I — X2 '
i2.a-x     + ax    a   ma + a -a   m a
sin x+cos x
(cos x — sin x)      10. 2
2 sin x tg* ln2
COS2 X
i.e'" sinbx 2.
x are sin x
(j _ x2)3/2     3' Ä - fcx2     4'a + b
cosx
5.Vx2 + a2 6.
6.4 tg5 x
11. -e^
2
are cos x
x2
7* I + X4
i. x*(ln x + 1)      2. x^ • x* • (ln2 x + ln x H—)      3. (sin x)
(lnx)tgx flnlnx + tgx )
V cos2 x     x ln x /
x
\I+COSX
(ctg2 x — ln sin x)
8
1.2xy + x2/;     2. (sin^y + cosy)y-y     y.y^{y — -72);     4- (3/ + 27 + i)y .