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Notes for DERIVATIVES with examples MATH 184 (UBC) CA$13.99
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Notes for DERIVATIVES with examples MATH 184 (UBC)
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Step-by-Step instructions on taking the derivative of: a constant, a variable raised to a constant, a polynomial function, a rational function, a radical function, trigonometric functions, a natural log function, a logarithmic function, an exponential function. Additionally, includes thorough expl...

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  • January 12, 2021
  • 3
  • 2020/2021
  • Class notes
  • Liu, keqin
  • All classes

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-

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

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