-
DERIVATIVES I
-
d-
( NO Variables)
o
of constant is
always O
=
ax a
•
E.ca/IC-z3/af-citI/ad-xCtej-- O
d -
°
Tx of a variable raised to a constant → IT CX
"
]nx
" "
¥
t front subtract I
exponent to
2×2
'
-
-
( XZ ]
more
2X
,
•
=
=
°
Fx of a variable raised to a constant X
by a constant
1-1 Tdy [ axb ] A # [Xb]
¥ [4×5]=4 # cxs]
= .
• . = 4.5×4=20×5
Constant multiple rule
comyma
°
Tdy of a
polynomial function → Tdy ( f- Cx)] =
"
f- CX)
• f- (x) = 4×3+7×2 - 9×+5
÷
?I Hmo!!
"
"
f- CX) 413×2) "×
-1¥?¥}
-
=
-
' '"" "
.
I'
=-3
to top
-
× variable
°
¥ of a rational function → Tdy [ =
pdx (X ]
- Z
=
-2×-30 ← simplify answer
② Use power
role
"
"
Cf ] #
-
Cx D= sx ←
finale
-
• = -
= = = =
.
off [ Ibs ) Tdy [-6*-9]=-6 - .
# (x D= -6C -
-
SX
-
7=30×-6 -
÷
D
-
.
"
of a radical
ree -ad×
function →
xiriius.no I Tdxcix ]=Td×Cx" '
EXCEED tacks) "J=ExCX"D= 5*3=55 "=s =1z=¥
=¥cx%]=¥x¥sxs=¥=a÷÷÷÷÷
=
Hanna'm
•
-
-
.
•
Excites ] ax
0¥
÷t÷÷÷÷÷÷iii÷÷÷÷
of
trigonometric functions [ sin u)
d
'
- -
-
Cosas .
U
i:¥÷÷÷÷i÷i÷÷:*
"
# 0M¥?? COSCX )
'
→
° .
3×2 u
'
. .
.
→ u ×
Similar
Sly ( b) = (O) (b) .
U
' o starts WIC = -0 o tan hot = Sec Icsc -1
.
.
o Sec Icsc = Sec tan Icsc tan -1
similar
Tdxccosx'T since)2x
odd-xcsecyfxu.fm =p 4seCl4Htan
•
→ -
I v=x 't U 2x
v.
'
-2XSN
-
, +
=
'
( Dou tandil
'
Asx Sin
Sec U
-
- -
.
Ex
Ctangex ?¥j%E×n5x4se
•
o
dot # xD] + →
ex 'tsxDcsocx > xD +
I V= × 3-1×5
3×2-15×4
'
, ' ' t
-
CSC CU) b -
v =
N°T^Tt°N°FDtFtE"""^
f- (x)
'
4
means -1
s the
'
'
f prime
derivative
of x
of
"
X
DERIVATIVES I
-
d-
( NO Variables)
o
of constant is
always O
=
ax a
•
E.ca/IC-z3/af-citI/ad-xCtej-- O
d -
°
Tx of a variable raised to a constant → IT CX
"
]nx
" "
¥
t front subtract I
exponent to
2×2
'
-
-
( XZ ]
more
2X
,
•
=
=
°
Fx of a variable raised to a constant X
by a constant
1-1 Tdy [ axb ] A # [Xb]
¥ [4×5]=4 # cxs]
= .
• . = 4.5×4=20×5
Constant multiple rule
comyma
°
Tdy of a
polynomial function → Tdy ( f- Cx)] =
"
f- CX)
• f- (x) = 4×3+7×2 - 9×+5
÷
?I Hmo!!
"
"
f- CX) 413×2) "×
-1¥?¥}
-
=
-
' '"" "
.
I'
=-3
to top
-
× variable
°
¥ of a rational function → Tdy [ =
pdx (X ]
- Z
=
-2×-30 ← simplify answer
② Use power
role
"
"
Cf ] #
-
Cx D= sx ←
finale
-
• = -
= = = =
.
off [ Ibs ) Tdy [-6*-9]=-6 - .
# (x D= -6C -
-
SX
-
7=30×-6 -
÷
D
-
.
"
of a radical
ree -ad×
function →
xiriius.no I Tdxcix ]=Td×Cx" '
EXCEED tacks) "J=ExCX"D= 5*3=55 "=s =1z=¥
=¥cx%]=¥x¥sxs=¥=a÷÷÷÷÷
=
Hanna'm
•
-
-
.
•
Excites ] ax
0¥
÷t÷÷÷÷÷÷iii÷÷÷÷
of
trigonometric functions [ sin u)
d
'
- -
-
Cosas .
U
i:¥÷÷÷÷i÷i÷÷:*
"
# 0M¥?? COSCX )
'
→
° .
3×2 u
'
. .
.
→ u ×
Similar
Sly ( b) = (O) (b) .
U
' o starts WIC = -0 o tan hot = Sec Icsc -1
.
.
o Sec Icsc = Sec tan Icsc tan -1
similar
Tdxccosx'T since)2x
odd-xcsecyfxu.fm =p 4seCl4Htan
•
→ -
I v=x 't U 2x
v.
'
-2XSN
-
, +
=
'
( Dou tandil
'
Asx Sin
Sec U
-
- -
.
Ex
Ctangex ?¥j%E×n5x4se
•
o
dot # xD] + →
ex 'tsxDcsocx > xD +
I V= × 3-1×5
3×2-15×4
'
, ' ' t
-
CSC CU) b -
v =
N°T^Tt°N°FDtFtE"""^
f- (x)
'
4
means -1
s the
'
'
f prime
derivative
of x
of
"
X
