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AP CALCULUS
1009: TRIG FUNCTIONS and e
Derivative of Sine -Graphically
sin( )y x
02
3
2
2
m m
m m
m
cos( )? ?y x
cos( )y x
Derivative of Sine - Analytically
REM: and 0
sin( )lim 1x
x
x
0
cos( ) 1lim 0x
x
x
sin( )d
xdx
Derivative of Cosine - Analytically
REM: and 0
sin( )lim 1x
x
x
0
cos( ) 1lim 0x
x
x
cos( )d
xdx
TRIG DERIVATIVES
TRIG Quotients and Reciprocal Identities:
tand
xdx
Likewise (cot )d
xdx
sin
cos
d x
dx x
TRIG DERIVATIVES
TRIG Quotients and Reciprocal Identities:
1(csc )
sin
d dx
dx dx x
Likewise dsec
dxx
TRIG DERIVATIVES
TRIG: Make List of Trig Derivatives …Memorize!
sin( ) cos( )
tan( ) cot( )
sec( ) csc( )
y x y x
y x y x
y x y x
Derivative of - Analytically
REM: 0
1lim 1
x
x
e
x
xde
dx
xe
Derivative of - Analytically𝑦=ln (𝑥)
y=lim𝑥→ 0
ln (𝑥)
y=ln (𝑥)
𝑒𝑦=𝑥
𝑒𝑦 𝑑𝑦𝑑𝑥
=1
𝑑𝑦𝑑𝑥
=1
𝑒𝑦=1𝑥
Therefore the derivative of
𝑦=ln𝑥
𝑦 ′=1𝑥
Think about
𝑦 ′=1𝑢∗𝑢 ′
y=ln (2𝑥+3)
𝑦 ′=1
2𝑥+3∗2
Last Update• 9/21/11
Assignment: p. 146 # 1 , 5 , 9 , 15 , 17 , 23