AP CALCULUS

1009: TRIG FUNCTIONS and e

Derivative of Sine -Graphically

sin( )y x

0232

2

m m

m m

m

cos( )? ?y x

cos( )y x

Derivative of Sine - Analytically

REM: and 0

sin( )lim 1x

xx

0

cos( ) 1lim 0x

xx

sin( )d xdx

Derivative of Cosine - Analytically

REM: and 0

sin( )lim 1x

xx

0

cos( ) 1lim 0x

xx

cos( )d xdx

TRIG DERIVATIVES

TRIG Quotients and Reciprocal Identities:

tand xdx

Likewise (cot )d xdx

sincos

d xdx x

TRIG DERIVATIVES

TRIG Quotients and Reciprocal Identities:

1(csc )sin

d dxdx dx x

Likewise d secdx

x

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 1x

x

ex

xd edx

xe

Derivative of - Analytically𝑦= ln (𝑥)

y=lim𝑥→0

ln (𝑥)

y=ln (𝑥)

𝑒𝑦=𝑥𝑒𝑦 𝑑𝑦

𝑑𝑥=1

𝑑𝑦𝑑𝑥=

1𝑒𝑦=

1𝑥

Therefore the derivative of 𝑦= ln𝑥𝑦 ′= 1

𝑥

Think about

𝑦 ′= 1𝑢 ∗𝑢 ′

y=ln (2𝑥+3)

𝑦 ′= 12𝑥+3∗2

Last Update• 9/21/11

Assignment: p. 146 # 1 , 5 , 9 , 15 , 17 , 23