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The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = (b) Incorrect: f'(x) = In the - sin(3x²). sin(3x²) (6x) (6).

The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = (b) Incorrect: f'(x) = In the - sin(3x²). sin(3x²) (6x) (6).

Calculus: Early Transcendentals
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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Numbers 6 & 8 please

6. Suppose you wish to diff What is the fastest way to do this, and why? 7. The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = (- sinx) (3x2)+(cos x) (6x). (b) Incorrect: f'(x) = sin(6x). 8. The derivatives of the function f(x) = cos(3x2) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = sin(3x²). (b) Incorrect: f'(x) = sin(3x²) (6x) (6). 9. In the proof that 1 dx √1-x² that sin(sin-¹ x) = x. It is also true that sin-¹ (sinx) = x could we have started with that inequality instead? Why || = | (x) + cos(x). (sin ¹x) = or why not? 10. Both of the following and tan-1 I we used the fact
Transcribed Image Text:6. Suppose you wish to diff What is the fastest way to do this, and why? 7. The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = (- sinx) (3x2)+(cos x) (6x). (b) Incorrect: f'(x) = sin(6x). 8. The derivatives of the function f(x) = cos(3x2) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = sin(3x²). (b) Incorrect: f'(x) = sin(3x²) (6x) (6). 9. In the proof that 1 dx √1-x² that sin(sin-¹ x) = x. It is also true that sin-¹ (sinx) = x could we have started with that inequality instead? Why || = | (x) + cos(x). (sin ¹x) = or why not? 10. Both of the following and tan-1 I we used the fact
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