, Differentiation
As recap -------
&
0
y
= 2xc -
3 ②
y
=
(20 3) (oc 1)
-
+
By =
dy =
4x
Ey =
2x2 -
x 3
- 304
dy
doc
= 40 -
1
da
= =
Y ea x
Y
=
ab
&
Nature of
Inx
&
-
loge
=
n logarithm
Rules :
"I
ex
⑳
y =
=
Y
S
Examples :
⑧
x2
⑤y
y In (3-2e)
2
edif
-
① y = = ze =
= dy 3e2-x (2x)
= -
- ( 6) 3x
+
-Exe2-x
S
=
dx
② 3e2
y
=
=
differentiate
=2Be
2x
Yet ⑨
y
= In (ex 2)
-
③y
+ = xe
= e
y e2 (4xd= 3
dx 4xe2
=
=
⑦ y In(x 2) = +
Le4x
-
④
y =x
=
yes 4x2 -1
=2
,Rules :
0
y
=
7 sinc
Sinc Coss
y y
= =
= Tcos
&y
= Cos
=- Since
- Cos() ④
②y 3sin(x) ③ cos
=
y
= =
y
=
=> differentiate d Z
y
= 3cos(
= Sin -since
=
2) Cos To = Sin =
Sinc
7
Given in booklet
:
tanxe seco ① Cot differed ② Cosec3t
Seco -secoctano y -Cose2tx2
=
dy
-
= -Cosec St Cot3tX3
dx
Cot -- Coseco -2Cose2t
=
do -
=
3 cosect cott
CoSex >
- -
Cosece Cot
③ tan (5x 3) + ⑦ Sin" (30)
Sin
(5
= 3))
100 Se
=
In (cose)
-do
⑤
& (sine) ⑥ 3Cosec( + )
tan-sh -Sinc
-
--tanx
= 3 coseco
cosa
* Coto
Cosa
=
tanx
, With Brackets :
①
② y (2x =
-
x + 3)3 ③ y (4x =
- x )
& & )
⑪
=
y = =
- 1(x 2)
2
-
=
-
(x 2)" 0
T2) = ( -
2xs)
= -E(7-2xs]( 0x) +
=
2 .
Sx4(7-2xS)
Product rule : xxy
Vitu
=
①
y =
c =
ex(1) + x(ex x 2x)
②y =
dy = Inx + 30 + +
5
=
ez 2x2ex +
-
do = 30nx+2
= ex(1 2x)) + =
x-(3)nx+ 1)
⑤ y = xtan2o ④y = eSince
tandetdase(2x)
&= yesinessa
⑤ y = Ge-2x Sin30 ⑥ -
3
*
Cosax
3xt
- 20
u= Se V = Sin 30 u = V= cos 20
= (zx )
20) =
V = -2 Sin 2x
u = -
2(ge v = 3c053 v =
2
=
-
=
=
10e
dy = -10 Sinda + Ge23cosse
Locos2a-bo Sin
-
&
do -10 Singa + 1Secosz0
=
=
=
Se2*(-2Sin3oc 3(os3x) +
= s(Ecos , - 6sin201)
As recap -------
&
0
y
= 2xc -
3 ②
y
=
(20 3) (oc 1)
-
+
By =
dy =
4x
Ey =
2x2 -
x 3
- 304
dy
doc
= 40 -
1
da
= =
Y ea x
Y
=
ab
&
Nature of
Inx
&
-
loge
=
n logarithm
Rules :
"I
ex
⑳
y =
=
Y
S
Examples :
⑧
x2
⑤y
y In (3-2e)
2
edif
-
① y = = ze =
= dy 3e2-x (2x)
= -
- ( 6) 3x
+
-Exe2-x
S
=
dx
② 3e2
y
=
=
differentiate
=2Be
2x
Yet ⑨
y
= In (ex 2)
-
③y
+ = xe
= e
y e2 (4xd= 3
dx 4xe2
=
=
⑦ y In(x 2) = +
Le4x
-
④
y =x
=
yes 4x2 -1
=2
,Rules :
0
y
=
7 sinc
Sinc Coss
y y
= =
= Tcos
&y
= Cos
=- Since
- Cos() ④
②y 3sin(x) ③ cos
=
y
= =
y
=
=> differentiate d Z
y
= 3cos(
= Sin -since
=
2) Cos To = Sin =
Sinc
7
Given in booklet
:
tanxe seco ① Cot differed ② Cosec3t
Seco -secoctano y -Cose2tx2
=
dy
-
= -Cosec St Cot3tX3
dx
Cot -- Coseco -2Cose2t
=
do -
=
3 cosect cott
CoSex >
- -
Cosece Cot
③ tan (5x 3) + ⑦ Sin" (30)
Sin
(5
= 3))
100 Se
=
In (cose)
-do
⑤
& (sine) ⑥ 3Cosec( + )
tan-sh -Sinc
-
--tanx
= 3 coseco
cosa
* Coto
Cosa
=
tanx
, With Brackets :
①
② y (2x =
-
x + 3)3 ③ y (4x =
- x )
& & )
⑪
=
y = =
- 1(x 2)
2
-
=
-
(x 2)" 0
T2) = ( -
2xs)
= -E(7-2xs]( 0x) +
=
2 .
Sx4(7-2xS)
Product rule : xxy
Vitu
=
①
y =
c =
ex(1) + x(ex x 2x)
②y =
dy = Inx + 30 + +
5
=
ez 2x2ex +
-
do = 30nx+2
= ex(1 2x)) + =
x-(3)nx+ 1)
⑤ y = xtan2o ④y = eSince
tandetdase(2x)
&= yesinessa
⑤ y = Ge-2x Sin30 ⑥ -
3
*
Cosax
3xt
- 20
u= Se V = Sin 30 u = V= cos 20
= (zx )
20) =
V = -2 Sin 2x
u = -
2(ge v = 3c053 v =
2
=
-
=
=
10e
dy = -10 Sinda + Ge23cosse
Locos2a-bo Sin
-
&
do -10 Singa + 1Secosz0
=
=
=
Se2*(-2Sin3oc 3(os3x) +
= s(Ecos , - 6sin201)
