= Republic of the Philippine

Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac
School: San Roque National High School Grade Level: 11
Teacher: RICHARD L. GALAG Learning Area: Basic Calculus
Observation Date: April 11, 2022 Quarter: 3 Observation: 1 2 3 4

Semi-Detailed Lesson Plan in Basic Calculus - Grade 11

(Scheduled Classroom Observation)

I. OBJECTIVES
A. Content Standard Basic Concepts of Derivatives
B. Performance Standard Formulate and solve accurately situational problems involving extreme values
C. Learning Competencies Derive the differentiation rules. STEM_BC11D-IIIf-2
Apply the differentiation rules in computing the derivatives of algebraic functions.
STEM_BC11D-IIIf-3
D. Objective Finding the derivative using power rule

II.CONTENT Rules in Differentiation

III.LEARNING RESOURCES
A. References
1. Teacher’s Guide pages
2. Learner’s Materials pages pp. 123 – 145
3. Textbook pages
4. Additional materials from SLM – Q3, Module 7
Learning Resource (LR)
portal
B. Other Learning Resources
Microsoft Mathematics Software, Geogebra

IV.PROCEDURES
A. Reviewing previous lesson Task 1.
or presenting the new Evaluate the LIMITS of the following expressions and reveal the answer by
lesson pulling out the puzzle on the board to see the picture of one of the Great
Mathematician.
1. lim
x→ 4
−3=−3

lim 3 x=−6
2. x→−2
lim x+ 5=3
3. x→−2

4. lim
x →1
(3 x)(5)=15

lim −( 2 x +1)(x +5)=−9

5. x→−2
x +5 7
6. lim =
x →2 3 x−2 4
x−25
7. lim =10
x →5 √ x−25
B. Establishing a purpose for The Derivative of a Constant
the lesson A constant function 𝑓(𝑥) is defined by 𝑓(𝑥) = 𝑐 or 𝑦 = 𝑐 and has a derivative
𝑓 ′ (𝑥) = 0 or 𝑦′ = 𝑐, respectively.
dy d
= (c )=0
dx dx
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac

The Power Rule

We start with the derivative of a power function, f(x) = x n. Here n is a number
of any kind: integer, rational, positive, negative, even irrational, as in x π . We
have already computed some simple examples, so the formula should not be
a complete surprise:
d n ( x +∆ x )n−x n
x = lim
dx ∆ x→ 0 ∆x

dy d n n−1
= x =nx where x >0
dx dx

For a specific, fairly small value of n, we could do this by straightforward

algebra.

C. Presenting Find the derivative of the following functions using Power Rule.
examples/instances of the d
1. 3x + 4
new lesson dx
d
2. 2x - 5
dx
d 2
3. x + 4x – 2
dx
d
4. 3x2 + 6x + 5
dx
d
5. 2x3 + 4x – 1
dx
D. Discussing new concepts Task 2.
and practicing new skills #1 Find the derivatives of the following functions using Power Rule.
d
1. 5x + 1
dx
d
2. 10x - 4
dx
d
3. 3x2 + 2x – 4
dx
d
4. 4x2 + 6x + 1
dx
d 3
5. x + 5x – 1
dx
E. Developing mastery
Task 3. PUZZLE DERIVATIVE!!!
See Attached Worksheet
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac

F. Finding practical Applications:

applications of concepts Suppose that a Covid 19 virus moves along a line with position function s’(t) =
and skills in daily living 2t2 + 3t + 1 where s is in meters and t in seconds
a. What is its initial position?
b. Where is it located after t = 2 seconds?
c. A what time is the particle at position s = 6?
Task 4. ASSESSMENT
G. Evaluating learning See Attached Worksheet

Teacher’s Attendance:

Name of Teacher Position Signature

RICHARD L. GALAG ROWENA T. MANIPON AMALIA D. LISING, EdD

Master Teacher II Head Teacher VI Principal III
Observer Observer

Reference: DepEd Order No. 42, s. 2016 (Policy Guidelines on Daily Lesson Preparation for the K to 12 Basic Educ. Program)
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac

LEARNING ACTIVITY SHEET

Subject: Basic Calculus Date:
Name: Date of Submission:
Grade & Section: Lesson No.: Activity No.:
Prepared by: RICHARD L. GALAG, Master Teacher II

Task 1. Evaluate the LIMITS of the following expressions. Match Column A with
Column B to reveal the answer by pulling out the puzzle on the board to see the picture
of one of the Great Mathematician.

4 6 5 1 7 3 2

Column A Column B
1. lim −3
x→ 4

N 10
lim 3 x
2. x→−2
I 3
lim x+5
3. x→−2
Z -6

4. lim ( 3 x ) ( 5) B -3
x →1

lim −( 2 x +1)(x +5) L 15

5. x→−2
I -9
x +5
6. lim
x →2 3 x−2 7
E
4
x−25
7. lim
x →5 √ x−25
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac
The Great Mathematician behind the Derivative of a Function Notation y = f(x) that can be denoted, such as
dy df (x)
f(x0, y, , , D f(x), or Dxf.
dx dx

RICHARD L. GALAG ROWENA T. MANIPON AMALIA D. LISING, EdD

Master Teacher II Head Teacher VI Principal III
Observer Observer

TASK 4 - ASSESSMENT
Subject: Basic Calculus Date:
Name: Date of Submission:
Grade & Section: Lesson No.: Activity No.:
Prepared by: RICHARD L. GALAG, Master Teacher II

***READ INSTRUCTIONS CAREFULLY BEFORE ANSWERING THE QUESTIONS***

*STRICTLY NO ERASURES *
I. MULTIPLE CHOICE: Choose the best answer. Blacken the circle that corresponds to your answer, USE the answer sheet.

1. Find the derivative f(x) = 5x + 3

a. 3 b. 5
c. – 5 d. 0
dy
2. 4x
dx
a. x b. 4
c. x4 d. 0
dy 2
3. 2x – 5
dx
a. 2x – 5 b. 4x
c. – 5 d. 4x2
4. If f(x) = 1, then find f’(x).
a. 1 b. 0
c. x d. – 1
5. If g(x) = π, then find g’(x).
a. π b. 0
c. x d. – π
6. Find the derivative of y = 2x3 – 2x2 + 4.
a. y’ = 2x2 – 2x + 4 b. y’ = 6x2 – 4x
2
c. 6x – 4x + 4 d. y’ = 6x2 + 4
3 2
7. Find the derivative of y = x – 4x + 7x – 3.
a. y’ = 3x3 – 8x2 + 7 b. y’ = 3x2 – 8x + 7
3 2
c. y’ = 3x – 8x – 3 d. y’ = 3x2 – 8x – 3
–6
8. Find the derivative of y = – 5x .
5 –5
a. y’ = b. y’ =
x6 x6
–1 5
c. y’ = 6 d. y’ = 5
5x x
3
dy 4
9. Evaluate x
dx
dy 4 dy 3
a. = 4 b. = 4
dx 3 √ x dx 4 √ x
dy 3 dy 3
c. = d. = 4
dx 4 dx √ 4 x
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac
10. Find the derivative y = πx.
a. 0 b. π c. 1 d. – 1

RICHARD L. GALAG ROWENA T. MANIPON AMALIA D. LISING, EdD

Master Teacher II Head Teacher VI Principal III
Observer Observer

ACTIVITY SHEET
Subject: Basic Calculus Date:
Name: Date of Submission:
Grade & Section: Lesson No.: Activity No.:
Prepared by: RICHARD L. GALAG, Master Teacher II

TASK 3 - DECODE THE MESSAGE

A message is hidden in the answer box. Follow these steps to decode the message.

Step 1 - Find the derivative using Power Rule in the Question Box.
Step 2 - Match the answer that you got with those found in the Answer Box.
Step 3 - Write the corresponding word below the correct answer in the Answer Box.

QUESTION BOX

TO NOT PERSON PRAY FOR

f(x) = 2x y = 4x - 3 y = 5x f(x) = 10 F(x) = - 3x2
; AN A BE STRONG
1 2
3
y = 2x – 4x 2 F(x) = 7 x 2 y = x3 f(x) = 2x - 5 f(x) = - 6x2 + 4x
PRAY EASY INSTEAD • LIFE
1
3 2 1
F(x) = x 2 y = 4 x3 f(x) = x - 5
y = 2π 4 3 f(x) = 5x2 - 7

ANSWER BOX

7 3
0 4 - 6x
2√ x 8 √x
PRAY NOT FOR AN EASY
8
10x 6x2 – 8x π 2
3 √x
3

LIFE ; INSTEAD PRAY TO

2 5 −6
- 10x -6 -6x 5 - x
3 √x
3
3
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac

RICHARD L. GALAG ROWENA T. MANIPON AMALIA D. LISING, EdD

Master Teacher II Head Teacher VI Principal III
Observer Observer

LEARNING ACTIVITY SHEET

Subject Date:

: Basic Calculus
Name: Date of Submission:
Grade & Section: Lesson No.: Activity No.:
Prepared by: RICHARD L. GALAG, Master Teacher II

Task 1. Evaluate the LIMITS of the following expressions. Match Column A with
Column B to reveal the answer by pulling out the puzzle on the board to see the picture
of one of the Great Mathematician.

4 6 5 1 7 3 2

Column A Column B
1. lim −3
x→ 4

N 10
lim 3 x
2. x→−2
I 3
lim x+5
3. x→−2
Z -6

4. lim ( 3 x ) ( 5) B -3
x →1

lim −( 2 x +1)( x +5) L 15

5. x→−2
I -9
x +5
6. lim
x →2 3 x−2 7
E
4
x−25
7. lim
x →5 √ x−25
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac

The Great Mathematician behind the Derivative of a Function Notation y = f(x) that can be denoted, such as
dy df (x)
f(x), y, dx , dx , D f(x), or Dxf.

ACTIVITY SHEET
Subject: Date:
Name: Date of Submission:
Grade & Section: Lesson No.: Activity No.:
Prepared by: RICHARD L. GALAG, Master Teacher II
= Republic of the Philippine
Department of Education
Region III – Central Luzon
Schools Division of Tarlac Province
SAN ROQUE NATIONAL HIGH SCHOOL
SENIOR HIGH SCHOOL
Bamban, Tarlac