MAC 2311C Lecture 1: Derivatives - chain rule
20 Jun 2018
School
Department
Course
Professor
Febuarg l3+h
Class notes
-
3.3 Derivatives of trig Functions
lim Sincxtmsnt → multiply out
h-20 n
\
sinx cosh + cos ...finish
•D
Lindo (shot)=he µis -
.case ,Sino '
rw + ano
D= (l,
+ an G)
o10 rq
•A
Area Of
OCB
=Area of OAB IArea OFOAD
¥
cos o Sino he
¥##i2<
¥tano
cososino to 2- tan o(Issing )
cos G EG- <
1-
-Cos G
Sino
lim lIf
vv
G-70 1squeeze (
I
✓
Example
l
Differentiate y= 1- 2Sin ×
X
"
sinx +×2sin× '
2× Sinx + ×2 cos ×#Check
E(cos ×)=-Sinx
dx
£+ an X=Sec 2× -Can find with
quotient race
Class notes Continued Feb 13in
a±×g×ux=±( cotsx )
=¥Po°jE#×
-l.#cosx =Ii )
cos 2×
=IF
=(s÷sIl(o÷s×)=tanxsecx
fcgcx ))=fog
T
first
3.4
Chain Rule :
F'Cx7 =f
'Cg (x)).gkx )
Example
F(x)=€1
F'Ct )= ÷(×2+ 1) 't • Zx
=
= sin (2×7 Ex e
-×
y
'= cos (2×7.2 =2cosC2x@
y
'
=f,)e- ×
=@
Example
y= 1×3+5×+714
y
'= 9(x3+5×+778
.(3×2+5 )
Y
'=4(
3×2+5 )(×3+5×+7 )8
