URV A7 f(x) = 2x2 + 4- r?B+? Q7 i?2 7QHHQrBM; Bb f ′(3)\

�X limh→0

2(3 + h)2 − 10

h"X lim

x→3

2x2 − 18

x − 3

*X limh→0

2(3 + h)2 + 18

h.X lim

x→3

2x2 + 18x

x − 31X lim

h→0

2h2 − 18

h − 3

UkV 6BM/ �HH p�Hm2b Q7 x 7Q` r?B+? i?2 ;`�T? Q7 f(x) =2x − 1

x + 1?�b � i�M;2Mi

HBM2 T�`�HH2H iQ i?2 HBM2 y = 3x + 1X

�X −2 �M/ 0 "X 3 �M/ 0 *X 0 �M/ 2 .X −3 �M/ 1

1X −3 �M/ 0

UjV � T�`iB+H2 Bb KQpBM; QM � bi`�B;?i HBM2 bQ i?�i Bib /BbTH�+2K2Mi 7`QK i?2Q`B;BM Bb ;Bp2M #v s(t) = t3 − 6t2 + 12t − 8X .m`BM; r?B+? Q7 i?27QHHQrBM; iBK2 BMi2`p�Hb Bb i?2 T�`iB+H2 bT22/BM; mT\

�X (2, ∞) QMHv "X (0, 3) QMHv *X (0, ∞) QMHv.X (0, 1) ∪ (2, ∞) 1X (0, 2) QMHv

U9V q?B+? Q7 i?2b2 bi�i2K2Mib �`2 h_l1\

UBV A7 f(x) = |x|- i?2M f ′(0) .L1

UBBV A7 g(x) =|x|x

- i?2M g′(0) .L1UBBBV A7 h(x) = x|x|- i?2M h′(0) = 0

�X PMHv UBV �M/ UBBV "X PMHv UBV *X PMHv UBV �M/ UBBBV.X LQM2 �`2 h`m2 1X �HH �`2 h`m2

U8V A7 i?2 MQ`K�H HBM2 iQ i?2 ;`�T? Q7 y = f(x) �i (2, 6) Bb y = 23x − 4-

r?�i Bb f ′(2)\

�X 32

"X 23

*X −32

.X 2 1X *�MMQi #2 /2i2`KBM2/

UeV :Bp2M i?2 ;`�T? Q7 y = f(x) �b b?QrM ?2`2,

0

y

x

y=f(x)

i?2M r?B+? ;`�T? #2HQr HQQFb KQbi HBF2 ;`�T? Q7 i?2 /2`Bp�iBp2 f ′(x) \

0

y yA

x x

B

00

y

x

C D y

x0

yE

0 x

UdV h?2 i�M;2Mi HBM2 iQ y =(2 +

√x)2

�i x = 1 BMi2`b2+ib i?2 y �tBbr?2`2\

�X (0, 6) "X (0, 4) *X (0, 2) .X (0, 1) 1X (0, 3)

U3V limx→0

tanπx

x secx=

�X1

π"X 0 *X 1 .X π 1X .L1

UNV 6BM/ i?2 /2`Bp�iBp2 Q7 f(x) =1

3√1 − x2

�X2x

3(1 − x2)13

"X−2x

3(1 − x2)43

*X−2x

3(1 − x2)13

.X2x

3(1 − x2)23

1X2x

3(1 − x2)43

URyV A7 y =√

x +√x- i?2M y′ =

�X1 +

√x

2√x +

√x

"X1 +

√x

4√

x +√x

*X1 + 2

√x

2√x +

√x

.X1 + 2

√x

2√x√

x +√x

1X1 + 2

√x

4√x√x +

√x

URRV :Bp2M i?2 7QHHQrBM; /�i�

f(0) = −3 f(1) = 4f ′(0) = 2 f ′(1) = 3

g(0) = 1 g(1) = 0g′(0) = −1 g′(1) = −2

-

B7 h(x) =f(g(x))

g(x)- }M/ h′(0)X

�X 7 "X 2 *X 4 .X 3 1X 1

URkVd2

dx2

(x sinx

)=

�X 2 cosx − x sinx "X x cosx + sinx *X x cosx − sinx

.X x sinx + cosx 1X x cosx − 2 sinx

URjV *QKTmi2 limx→0

sinx cosx − sinx + x sinx

x2

�X 12

"X .L1 *X 0 .X 2 1X 1

UR9Vd

dx

(sin3(x) − cos(x3)

)=

�X 3 sin2(x) cos(x) − 3x2 sin(x3)

"X 3 sin2(x) cos(x) + 3x2 sin(x3) cos(x3)

*X 3 sin2(x) cos(x) − 3x2 sin(x3) cos(x3)

.X 3 sin2(x) cos(x) + 3x2 cos(x3)

1X 3 sin2(x) cos(x) + 3x2 sin(x3)

UR8V lb2 AKTHB+Bi .Bz2`2MiB�iBQM iQ }M/ y′ B7 x2 + 5xy − 6y4 = 18

�X2x + 5y

24y3 − 5x"X

2x + 5y

24y3*X

2x

24y3 − 5x

.X2x + 5y − 18

24y31X

2x + 5y − 18

24y3 − 5x

UReV lb2 GQ;�`Bi?KB+ .Bz2`2MiB�iBQM iQ }M/ i?2 /2`Bp�iBp2 Q7 f(x) = xsinx

�X (sinx)xsinx−1 "X xsinx (cosx) (lnx)

*Xsinx

x+ (cosx) (lnx) .X xsinx

[sinx

x+ (cosx) (lnx)

]

1X x cosx + sinx

URdV A7 f(x) = xlnx- }M/ f ′(e)X

�X 0 "X 1 *X 2 .X 3 1X 4

UR3V A7 y = x2 + 2x- i?2Mdy

dx=

�X 2x + x2x−1 "X 2x + 2x *X 2x + 2x ln 2

.X (2x + 2x) ln 2 1X 2x +2x

ln 2

URNV 6BM/ f ′(1) B7 f(x) = ln

[(3x − 1)2

(x + 1)4

]

�X 1 "X −1 *X 2 .X −2 1X 5

UkyV A7 f(x) = tan−1

(2

x2

)- f ′(−1) =

�X 1 "X4

5*X −

2

5.X

2

51X −

4

5

UkRV A7 y = arcsin(x) −√1 − x2-

dy

dx=

�X1

2√1 − x2

"X1 + x

√1 − x2

*X2

√1 − x2

.Xx2

√1 − x2

1X1

√1 + x

UkkV *QKTmi2 y′′ B7 x2 + y2 = 2y + 5X

�Xd2y

dx2=

1

1 − y+

x2

(1 − y)2"X

d2y

dx2=

1

1 − y+

x2

(1 − y)3

*Xd2y

dx2=

1 + x2

(1 − y)2.X

d2y

dx2=

1 + x2

(1 − y)3

1Xd2y

dx2=

x2

1 − y−

1

(1 − y)3

UkjV A7 y = y(x) Bb /2}M2/ BKTHB+BiHv #v i?2 2[m�iBQM y ey2= 10x-

i?2Mdy

dx=

�X y + 2yey2 "X 2y2ey

2+ ey

2 *Xy

x(2y2 + 1).X

y

(2y2 + 1)

1Xy

10(2y2 + 1)

�Mbr2`b

RX " kX � jX � 9X 1 8X * eX 1 dX � 3X . NX 1RyX 1 RRX 1 RkX � RjX 1 R9X 1 R8X � ReX . RdX *R3X * RNX � kyX " kRX " kkX " kjX * k9X .