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Teacherbot 27 Mar, 15:02:08

Lesson Title: Chain Rule with Derivatives of Trigonometric, Exponential, Logarithmic Functions

Learning Intention: Students will be able to apply the chain rule to find the derivatives of functions that involve trigonometric, exponential, and logarithmic functions.

Introduction (5 minutes): Begin the lesson by reviewing the chain rule and its importance in finding the derivatives of composite functions. Ask students to recall the formula for the chain rule and provide an example of a composite function that requires the chain rule to find its derivative.

Body (40 minutes): 1. Derivatives of Trigonometric Functions: Explain to students that the derivatives of trigonometric functions can be found using the chain rule. Provide examples of functions such as sin(2x), cos(3x), and tan(4x) and ask students to find their derivatives using the chain rule. Emphasize the importance of using the derivative of the outer function and the derivative of the inner function in the chain rule formula.

  1. Derivatives of Exponential Functions: Next, introduce the derivatives of exponential functions and how they can be found using the chain rule. Provide examples of functions such as e^(2x), 3^(4x), and 5^(x^2) and ask students to find their derivatives using the chain rule. Remind students to use the derivative of the outer function and the derivative of the inner function in the chain rule formula.

  2. Derivatives of Logarithmic Functions: Finally, introduce the derivatives of logarithmic functions and how they can be found using the chain rule. Provide examples of functions such as ln(2x), log(3x), and ln(x^2) and ask students to find their derivatives using the chain rule. Emphasize the importance of using the derivative of the outer function and the derivative of the inner function in the chain rule formula.

Conclusion (5 minutes): Summarize the key points of the lesson and ask students to reflect on their understanding of the chain rule with derivatives of trigonometric, exponential, and logarithmic functions. Provide additional practice problems for students to work on independently or in groups.