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4. Guided Proof: Consider the function f(r) = tan(r), and remember that tan(r) = sinz You will derive the derivative of tan(r). Cos r (a) What is the domain of f? (b) Use the quotient rule to show that one expression for f'(x) is: cos(r) cos(x) + sin(x) sin(x) f'(1) = cos? r (c) What is a Fundamental Trigonometric Identity involving cos(r) and sin(x)? Use it to simplify f'(x). (d) Recall that sec(r) = How can we express f'(x) in terms of the secant function? Thus, what is the final simplified form of the derivative of tan(r)? Cos z (e) For what values of r is f'(x) defined? How does this set compare to the domain of f?

4. Guided Proof: Consider the function f(r) = tan(r), and remember that tan(r) = sinz You will derive the derivative of tan(r). Cos r (a) What is the domain of f? (b) Use the quotient rule to show that one expression for f'(x) is: cos(r) cos(x) + sin(x) sin(x) f'(1) = cos? r (c) What is a Fundamental Trigonometric Identity involving cos(r) and sin(x)? Use it to simplify f'(x). (d) Recall that sec(r) = How can we express f'(x) in terms of the secant function? Thus, what is the final simplified form of the derivative of tan(r)? Cos z (e) For what values of r is f'(x) defined? How does this set compare to the domain of f?

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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sin z 4. Guided Proof: Consider the function f(r) = tan(x), and remember that tan(r) = You will derive the derivative of tan(r). Cos r (a) What is the domain of f? (b) Use the quotient rule to show that one expression for f'(x) is: cos(r) cos(x) + sin(x) sin(r) f'(1) = cos? r (c) What is a Fundamental Trigonometric Identity involving cos(r) and sin(x)? Use it to simplify f'(x). (d) Recall that sec(r) = How can we express f'(x) in terms of the secant function? Thus, what is the final simplified form of the derivative of tan(r)? COS I (e) For what values of r is f'(r) defined? How does this set compare to the domain of f?
Transcribed Image Text:sin z 4. Guided Proof: Consider the function f(r) = tan(x), and remember that tan(r) = You will derive the derivative of tan(r). Cos r (a) What is the domain of f? (b) Use the quotient rule to show that one expression for f'(x) is: cos(r) cos(x) + sin(x) sin(r) f'(1) = cos? r (c) What is a Fundamental Trigonometric Identity involving cos(r) and sin(x)? Use it to simplify f'(x). (d) Recall that sec(r) = How can we express f'(x) in terms of the secant function? Thus, what is the final simplified form of the derivative of tan(r)? COS I (e) For what values of r is f'(r) defined? How does this set compare to the domain of f?
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