Explanation Given: The function, y = ln sin x − 1 2 sin 2 x . Concept Used: The product rule of derivatives: d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 d d x ( ln x ) = 1 x d d x ( sin x ) = cos x Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: In order to find the derivative of the function, use chain rule andpower rule of derivatives and simplify further to get y ' = d d x ( ln

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3, Problem 39E

To determine

The derivative y' of the function, y=lnsinx−12sin2x .

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Chapter 3, Problem 38E

Chapter 3, Problem 40E

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The derivative y ' of the function, y = ln sin x − 1 2 sin 2 x .

Solution Summary: The author explains how to find the derivative of the function using chain rule and power rule of derivatives.

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The derivative y' of the function, y=lnsinx−12sin2x .

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Chapter 3 Solutions