AP Calculus BC
Reference Page
Basic Differentiation Rules
d
[cu ] = cu '
dx
d
3.
[uv ] = uv '+ vu '
dx
d
5.
[c ] = 0
dx
d
7.
[ x] = 1
dx
1.
9.
11.
13.
15.
17.
d
u'
[ln u ] =
dx
u
d
[sin u ] = ( cos u ) u '
dx
d
[ tan u ] = ( sec2 u ) u '
dx
d
[sec u ] = (
AP Calculus BC - Worksheet
Derivatives of ln and e
27 Know the following
theorems:
1.
2.
Examples
1.
Find
2.
3.
.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. A line with slope m passes through the origin and is tangent to
18. Evaluate
. Wha
AP Calculus BC Worksheet 30
LHopitals Rule
Evaluate each Limit. Use LHopitals Rule where appropriate.
Find each derivative.
9
f ( x) = e x
10
y = e4 ln x
11
y = 3x+1
12
y = 4x 2 + 4x
13
g ( x ) = cos 3 5x
14
y = ln xe2 x
15
y = ln sin x
16
f ( x ) = x cot
AP Calculus BC - Worksheet 18
Power Rule
Nearly all men can stand adversity, but if you want to test a man's character, give him power. - Abraham Lincoln
( ) ( )
Learn: The Power Rule: f x = a
a
()(
)
1
d
Example:
Use the Power Rule to find the derivat
AP Calculus BC Worksheet 22
1
Derivatives (Power, Package, Product and Quotient Rules) Review
Use the limit definition of the derivative to find f ' ( x ) for f ( x ) = 2x 2 + 1
Find the derivative of each function below.
2
2x
y=
3x + 1
3
2
y=
( 5x + 1)3