CCF20081211004

c

438

Rozwiązania i odpowiedzi

-12

x~ 3\/x

-3/2

DO ROZDZIAŁU VI

6.45. y' = x²(l — 6x + 13x² — 12x³)

6.47. / = 3ax² - -₂ .

x²

6.49. y' = 63x⁶-15x"⁶+33x 6.51. x*0, y' = -57= •

5Vx³

1 , ¹

6.53. x>0, y =jy= —3x +-47^=

Vx    2V*

-4    1

6.55. x>0, y' = -jj=-_7T7= 6.57. *>0, x'=y 7? .

6.46. y' = 75x¹⁴ —2x + |.

12

6.48.

X⁴

6.50. /-=7x^4,*-13x*'⁴-yX 6.52. y' = -V7⁴.

6.54. x>0, y' = —--śj=-3jx.

2\]x 2 yjx

-5    ₆    3

6.56. x>0, y' = —7-7= —14x⁶--7=

1 yf X⁶    4 VX³

-7

6.58. x^0, y — ₍ .r-%9 '

6.59. y'= 16x —3x² .

6.60. y' = 24x²+§7**

6.61. x^$, y' =

-9

(3x —2)

2 •

6.62. 2x²-5x + 1^0, y'= —5

— 20x+25

(2x² —5x + l)

6.63. 7x⁵ — x + 2/0, y' =

— 3x(21x⁵ + x —4)

(7x⁵ —x + 2)

6.64. x³+x-l*0. y'= —

,    8x²(2x - 3)

(x³ +x —1)

2 ‘

6.65. x^l, y' =

-4

(x-l)

6.66. y —

-x²+74x+7

(x²+7)^2_

4x(x—3)

6.67.    -3, jc#1, y'=_(x+3)2(*_!')*•

_t — 6x(l+3x—5x³) 6.68. x^±l, x^7i» y ⁼(₁__x2)²(i_2x³)²

1

6.70. />0, z' —

1-72

6.69. *>0, x^l.    * =2^(1 W*)’ '

6.72. t/ = 5(4z² —5z + 13)⁴(8z —5) .

6.71. s' = 21 (3* + 1)⁶ .

6.73.    r^O, ^{x, =} -p-^7⁺⁴) *

6.74.    *#0, s' = 6^14* + ^^7/²-y+6^

«.75 jx|>2, y = ^4= •

Vx — 4

6.76. ox² + 5x+c>0, z' =

2ax+b

2yjax* +bx+c

6.77. /<§, / = §•

(V2-3r)³ '

6.78. 0<f<6, s' =

1 — 3

(■s/6t-t²)³

6.79. / =

4x

y(2-x³)⁷“

P~ 1

" V(n+6x)^p+n

6.81. / =

pnx‘

(b-xy*¹

6.82. x>l,    -

1

6.83. a t^O, u'=

1

Ja² +v²(v—\l a² + u²)

6.84. — a<x<a, _y' =

— a

(a+x)\/(a+x)(a-x)

6.85. a² —z²>0, u' =

a

nV-z²)^j'

6.86. x>0, y' =

3(1-3x²) 2v/x(x² + l)²‘

6.87

tf/x³ + l)‘

6-88. (x—l)(x—2)(x—3)(x—4)>0, z' =

2x² + 10x—11

6.89. x^a, z

2a²x

(x—3)(x—4)V(x— l)(x—2)(x—3)(x—4)

-1

(a² +x²)yJa^Ą—x^Ą

6.90. I 1, s' =

2(i+VóVf(i-o

. ,^±i_f

u² V 1-y²

6.93. a9^0, y' =—-sin —.

a a

6.92. y^uW + uł/w+wyw'.

6.94. x' = ab cos bt.

—a    a

6.95. Xi*0, y' = —=-cos —.

X    X

6.97. s' = 3 sin 6t.

4 sin t

6.99.    cos/^0, s' =—=-•

cos⁵1

,    .    , — 30cos2f

6.100.    sin2ft^O, u ——_r-_s-

sin 21

6.96. z'=4cos²x.

6.98. v' = — 5 sin j f cos⁴ \ t

6.101. sin 2f ?60, s' =

sin³ i—cos³ t

sin² 21