Explanation Given: q ( x ) = sin ( θ ) 1 + cos ( θ ) Concept Used: Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where g is a differentiable function at x and f is a differentiable function at g ( x ) Product rule of differentiation formula d d x ( u v ) = v d d x u + u d d x v Power rule of differentiation formula d d x x n = n x n − 1 d d x sin x = cos x d d x c o s x = − sin x Calculation: To find derivative of the function q ( x ) = sin ( θ ) 1 + cos ( θ ) Differentiate both sides as d q ( x ) d x = d d x [ sin ( θ ) 1 + cos ( θ ) ] = d d x [ sin ( θ ) ( 1 + cos ( θ ) ) − 1 ] Now use product rule of differentiation to solve it further, that is, d d x ( u v ) = v d d x u + u d d x v Here, u = sin θ ; and v = ( 1 + cos ( θ ) ) − 1 Thus, q ′ ( x ) = d d x [ sin ( θ ) ( 1 + cos ( θ ) ) − 1 ] = sin ( θ )

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 2.10, Problem 4E

To determine

To find derivative of the function

q(x)=sin(θ)1+cos(θ)

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Chapter 2.10, Problem 3E

Chapter 2.10, Problem 5E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - 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To find derivative of the function q ( x ) = sin ( θ ) 1 + cos ( θ )

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To find derivative of the function q(x)=sin(θ)1+cos(θ)

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Chapter 2 Solutions

To find derivative of the function

q(x)=sin(θ)1+cos(θ)