pochodne odpowiedzi

494

Odpowiedzi do zadań

1 Rozdział 6

495

-¹

6.50.    /'(ar)

6.51.    /'(ar)

6.52.    /'(ar)

6.53.    /'(ar)

6.54.    /'(ar)

6.55.    /'(ar)

6.56.    /'(ar)

6.57.    /'(ar) =

6.58.    f'(x) =

6.59.    /'(ar) =

6.60.    /'(ar) =

6.61.    /'(ar) =

6.62.    f'{x) =

6.63.    /'(x) =

6.64.    f'(x) —

6.79.    /'(ar) =

6.80.    /'(ar) =

6.81.    /'(ar) =

6.82.    /'(z) =

6.83.    /'(ar) =

6.84.    /'(ar) =

6.85.    /'(z) =

6.86.    f'{x)

6.65.    f(x) = 15e^3a:sin'¹(e^3a:) cos(e^3a:).

6.66.    f(x) = ctg(x+ Ą) (1 - 4,).

6.67.    =

6.68.    =

6.69. /'(a;) = ^_tg(^)-6 70 /•'far') = ²*0+tg²(*²))

6.71.    /'(a:) = 6sin4arsin2are^2sin32*.

6.72.    =

6.73.    /'(i) =

6.74.    /'(i)

6.75.    /'(*) = ^"y).

6.76.    /(*) =|^r.

6.77.    /'(a;) = 12ar²sin(4ar³)sin²(2ar³).

6.78.    /'(*)=■£$!•

—3cos²(51n(x² ł- 1) -(- x)sin(51n(:r² 4- 1)    + 1V

(e^x—e~^xp ‘

3(sin²arcosar 4- a:² cos(ar³)).

inaj-c

_    2 COS a

cos² x—2sinx—2 ‘

4a(a⁴—1) (a⁴+a²+i)^ ‘

_ 2_

(l+a²)(l—arctga)'

_ 4 tg² a

sin2a ‘

| 6.89. f'(x) 6.90. /'(a?)

_ 2(tg²a+l)

- "Wr-_ ^s»ⁿ^V^p

1 —cos² a

6.91. /'(ar) ---

3a(ł+ln a)² y (

« OQ    — (l+tg²a)|l+tga

D.yj. / (arj - ^T^i+tga)²

l-lnxN² ' 1+ln x)

arc ctg (3a))²    ‘

_ 2arc8in(2a—y/l—a² arcsina) •/l—a² (a—arc sin² x)

_ 4e^2x

1

1—a² ‘

_ 2cos2.a—3ain2a

^3x    •

_ 2-9^x(l — x In9)

^_    (a+9^x)^2    -

- 2(lnasin2a—

(Ina—sin² a)²    *

= 6 sin 6ar.

= —6 cos² 2orsin 2ar.

= —6sin6ar.

—30a arc cos ⁴ (3a²)

\/l—9a⁴    ’

asina+cosa

2

" VP+T'

COB X

e * .

³ sin (2 ln(2ar + 1)) sin (ln(2ar + 1)).

2a+l

In3sin(2a) ln 2    •

_ 2 cos a'

6.94. /'(ar) = 4ar/3(l 4- ar²)² -³/(

l+a'

ln 2    <

ay1—ln² a

arcsinlna

6.87.    f(x) =

6.88.    /'(i) = fa.

6.95. /'(ar)

6.97.    /'(ar)

6.98.    /'(ar) =

6.102. /'(ar)

| 6.103. /'(ar)

l 6.104. /'(ar)

| 6.105. /'(ar)

6.106.    /'(ar)

6.107.    /'(ar) =

6.108.    /'(ar) =

6.109.    /'(ar) =

6.110.    /'(ar) =

6.111.    /'(ar) =

(    6.112. /'(ar) =

| 6.113. /'(ar) = | 6.114. /'(ar) =

5 6.115. /'(ar) = | 6.116. /'(ar) = |§ 6.117. /'(ar) =

l-fe'

m

¹ 3 ln 2(a² —1) *

1

w

_3sin²acoBa-\/l+sin³a

(1+sin³ a)²y'7—sin³ a

(l+a²

⁶-⁹⁹- A*) =

6.100.    /'(ar) = ^_x^_Wl+xi ■

6.101.    /'(ar) =ar*(lnar4-l).

= (sin ar)* (ln(sinar) 4- arctgar).

= (l + i)«(Ml + |)-rf;).

(^»? + ^5«).

= (sinar)⁰⁰³* (cosarctgar - sinarln(sinar)).

= (lnar)^ctga: (^

^v '    ^alna    sin² a

—    2z^lnxIna

X

—    _cXgx / Ina , tga\

\ COS² X ^r X ) •

= (arctg*)* (ln(arctgx) +

= -(cosz)*™'””* (J^^ + arccosxtgx).

—    (1 — 21nar) • a?(* ^2_3).

1—actgalna .    *

xs\nx ^

(1 — lnar) • ar^«^-2\

ar**ar* (lnar(lnar + 1) + j).

(arctgX)*¹”²* (sin(2x) ln(arctgx) +

(sin²ar)^ctg* (2ctg²ar - ln(sin²ar)(l + ctg²ar)).

— (cos ar²)^ctg* (ln cos ar² (1 + ctg ²ar) + 2ar ctg ar tg ar²).

r