Further Mathematics - Senior Secondary 2 - Differentiation of Transcendental Functions

Differentiation of Transcendental Functions

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TERM: 2ND TERM

WEEK: 2
Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Differentiation of Transcendental Functions
Focus: Differentiating transcendental functions such as sin x, e^ax, and log(3x)

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Differentiate the function sin x with respect to x.
  2. Differentiate the function e^ax with respect to x.
  3. Differentiate the function log(3x) with respect to x.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Analogy and real-life applications

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Chart showing areas of application for transcendental functions (e.g., physics, engineering)
  • Graphing calculator or graphing software (optional)

 

PERIOD 1 & 2: Introduction to Transcendental Functions and Differentiation

PRESENTATION:


              2. Differentiate e^(x+1).

              3. Differentiate log(5x).

              4. Find the derivative of e^(2x).

              5. What is the derivative of sin 4x?

ASSIGNMENT (5 tasks):

  1. Differentiate e^(4x).
  2. Differentiate log(7x).
  3. Find the derivative of sin 5x.
  4. Differentiate e^(ax).
  5. Solve: d/dx (log(6x)).

 

PERIOD 3 & 4: Application and Practice of Differentiation

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Application in Real Life

Discusses real-life applications of transcendental functions and their derivatives (e.g., rate of change of oscillations, growth/decay models in biology and physics).

Students listen and take notes on real-life applications.

Step 2 - Guided Practice

Provides a set of mixed problems involving the differentiation of sin x, e^ax, and log(3x) for students to solve with teacher guidance.

Students solve problems individually or in pairs, asking questions as needed.

Step 3 - Independent Practice

Assigns additional problems for students to complete on their own. Provides assistance as needed.

Students complete exercises independently and submit them for evaluation.

NOTE ON BOARD

Example Problems:

  
  • Differentiate sin(2x).
  • Differentiate e^(3x).
  • Differentiate log(4x).
    Review and summarize key concepts covered in the lesson. | Students copy examples and solve exercises in their notebooks. |

EVALUATION (5 exercises):

  1. Differentiate sin 2x.
  2. Differentiate e^(x+2).
  3. Differentiate log(5x).
  4. What is the derivative of sin 6x?
  5. Differentiate e^(x²).

CLASSWORK (5 questions):

  1. Differentiate sin 3x.
  2. Differentiate e^(4x).
  3. Differentiate log(8x).
  4. Differentiate e^(x+5).
  5. Find the derivative of sin 7x.

ASSIGNMENT (5 tasks):

  1. Differentiate e^(5x).
  2. Differentiate log(9x).
  3. Find the derivative of sin 8x.
  4. Differentiate e^(ax).
  5. Solve: d/dx (log(2x)).