f(z) = sin f'(z) = Let 9(z) = sin z g'(z) = %3D 117

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image contains mathematical text and expressions for educational purposes. Here is the transcription:

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**Function Definition and Differentiation Problem**

Given the function:

\[ f(x) = \sin\left(\frac{1}{x}\right) \]

We are asked to find its derivative, denoted as \( f'(x) \). There is a placeholder (a rectangular box) to enter the derivative:

\[ f'(x) = \boxed{} \]

Next, we are provided with another function definition:

Let 

\[ g(x) = \frac{1}{\sin x} \]

Similarly, we are required to find the derivative of this function, denoted as \( g'(x) \). There is also a placeholder for entering this derivative:

\[ g'(x) = \boxed{} \]

---

This transcription is designed to be used in an educational context, allowing students to practice differentiation of trigonometric functions and their compositions.
Transcribed Image Text:The image contains mathematical text and expressions for educational purposes. Here is the transcription: --- **Function Definition and Differentiation Problem** Given the function: \[ f(x) = \sin\left(\frac{1}{x}\right) \] We are asked to find its derivative, denoted as \( f'(x) \). There is a placeholder (a rectangular box) to enter the derivative: \[ f'(x) = \boxed{} \] Next, we are provided with another function definition: Let \[ g(x) = \frac{1}{\sin x} \] Similarly, we are required to find the derivative of this function, denoted as \( g'(x) \). There is also a placeholder for entering this derivative: \[ g'(x) = \boxed{} \] --- This transcription is designed to be used in an educational context, allowing students to practice differentiation of trigonometric functions and their compositions.
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