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TEACHER:
A Rehman
Charles H. Milby High School
Weekly Lesson Plan
SUBJECT(S):
Ap Calculus AB
Week#1
OBJECTIVES
MONDAY
AIM VIA INQUIRY
WEEK OF:
Sep.30-Oct 4
THURSDAY/FRIDAY
To use chain rule to find the derivatives.
To find the derivatives of Trigonometric
functions
ELPS: C.4d Use pre reading supports
such as graphic organizers,
illustrations, and pre taught topicrelated vocabulary and pre reading
activities to enhance comprehension
of written text.
ELPS: : C.4d Use pre reading supports
such as graphic organizers, illustrations,
and pre taught topic-related vocabulary
and pre reading activities to enhance
comprehension of written text.
ELPS: C.3d Speak using grade-level
content area vocabulary in context to
internalize new English words and build
academic language proficiency.
d 2 d 5
[x ]  [x ]
dx
dx
4
 2 x  5 x  10 x 5
Suppose that the function
10 x  7 x
the population of a city
6
You can see that the derivative of a
product is not generally the product of
corresponding derivatives.
So how can we evaluate the derivative
of the product, for instance;
ln x  2x
Sentence Stem: The derivative of a
product is------- the product of the ------------..
P(t )  100  8t models
after t years. What is
the rate of growth of that
population after 2 years?
Look at sine and cosine functions. They are
continuous and periodic.
Name some more real life examples that are
periodic, and hence in describing those
processes, trigonometric functions may be
utilized.
How would you find rate of change of these
functions. In other words the Derivative of
trigonometric functions.
The only way we know is to take the limit
of each function when h is approaching
zero.
Sentence Stem: When two or more ---------Are combined its called ----------.
Sentence Stem: The sine and cosine
functions are -----------. They repeat after -------------.
Combine two given functions to form a
new function.
Graph sine and cosine functions on the
same axis.
Observe that in each case, we have brought
the exponent down, lowered the power by
one and then multiplied by 2x, the derivative
Now graph the functions sinx, and cosx in
your calculator at the same time and verify
that the slope f” of f, sinx is indeed cosx.
Then graph cosx and –sinx and verify that f
is cosx and its derivative is -sinx.
Find the rate of change:
2 x3  x
f ( x) 
, at x =1
x3
2
AGENDA
1
To use product and quotient
rules.
5
Warm-up /DO
NOW
TUESDAY/WEDNESDAY
6-Weeks
Cycle:
Product
d
[ f ( x) g ( x)]
Rule: dx
 f '( x) g ( x)  g '( x) f ( x)
of x
Rule.
 1 . This is an example of Chain
d
[ f ( g ( x)) 
dx
f '( g ( x)) g '( x)
d
[sin x] 
dx
sin( x  h)  sin x
lim
h 0
h
 cos x, Similarly
d
[cos x]   sin x
dx
EXIT TICKET
Find the derivative of;
y  ( x4  3x2 )( x3  4 x)
Find the derivative of
the expression for an
unspecified differentiable function f ( x).
f ( x2 )
f ( x)
4 f ( x)  1
Use the limit process and prove the
following.
d
[tan x]  sec 2 x
dx
d
[cot x]   csc 2 x
dx
d
[sec x]  sec x tan x
dx
d
[csc x]   csc x cot x
dx