CCF20081211001

Zadania 115

6.105. 3>=cosx—| cos³x. 6.107. y=tg^Ąy/x.

6.109. y — e^ax(asinx~ cosx)

6.106. y=\ sin³x— § sin³x+ ~ sin⁷x 6.108. y = 3ctgx+ctg³x.

6.111. y=cos^:

£

6.110. y=x²e^2xsinx.

sin x 2

6.113. y ₇ c 5 * cos x 5 cos x

3cos²x

6.114. y=—r-j

sin x

6.115. y= sin x+\Jx+2y/x.

6.116. y— 1 H-tg( x +

6.117. z —

3 tg u —tg³ u 1 — 3 tg² u

6.118. z = tgw —ctgw —2u.

6.119.    y = (4sinx — 8sin³x)cosx.

6.120.    y=arctg 3x.

6.122. x=arcsin (1 — f).

6.124. x = arcsin\/7³.

6.126. y — arcsinx +arcsinV1—x²,    0<x < 1.

6.121. _y = 7arctg|x. 6.123. x = arccos\/l — t².

6.125. x = arcsin — .

t

6.127. x = arcsin 2t\]l — t².

6.129. y=arctg >/x² — l —

lnx

6.131. y= j x⁵ arctg x - ^x⁴+^x²-^ ln (1+*²)-

6.128. >> = arctg (x —\/x² +1). 6.130. }>=x arctg x — |ln(x²+l)

6.132. y = arcsin

Vl

+x

6.133. j;=arccos

1 —x l+x

6.134. y = arctg

1 —x l+x

1 +x

6.135. y=arctg --, x ^ 1.

1 — x

6.136. y — arctg

1 Wl+x

6.137. y = arctg

V1+X² -1

6.138. y=

arctg 2x arcctg 2x

6.139. z=

1 — arcsin y 1+arcsin .y

6.140. y=x³ arctgx³.

6.141.

2 —

arcsin 4 y 1-4 y

6.142. y —

6.143. y=

1

■ _r- arcsin

a cos x + b ^•

n+6cosx

-6.144. y = e^3x.

6.146. y = e^xf(x).

-6.148. y = e^sinx.

-6.150. y = e^cosJx.

6.152. z = (u³ — 3u² + 6u — 6) e”.

6.145. y = 5<?*^x.

6.147. y = 3<T^2x£(x). 6.149. y = 5e^cosx.

6.151. y = 3e^2sin,x. 6.153. z = (10x² —l)e^3x.

6.154.

(2x-l)e*

2\fx ‘

6.156. y = 5^x+2^x.

6.158. y = 2 • 7^X— 1.

6.160. y=a^2xxⁿ ,    a>0.

6.155. y = (x+kyfl—x²)e^k*^rc*^lttx.

6.157. y — 3^xx³.

6.159. y = 5 - 10^3x.

6.161. y = ln3x.

6.162. y = 7-5^10x.

6.163. z = ln

30 x+3

6.164. y = 51n 10x.

6.165. s = In(/+V/²+l).

6.166. z = 3In

x —2

6.167. s = In

1+t

6.168. y = 2 In

t+yjt²-4

6.169. y = ln |ln |x||.

6.170. y

=inf^{a + fctgX}V

Vz-fctgx/

6.171. y=lntg(|ji+|x), 0<x<

KłlM

6.172. y = ln (cos \x)².

6.173. y=ln

1 +sinx 1 — sin x

COS X

6.174. y=151ntg|x + -_r^—(8cos⁴x-25cos²x + 15).

sin x

6.175. y = ln(ln(lnx)),

x>e.

6.176. y = ln

yjx² +1

V7+l

+x