Explanation Given Information: The function is z ( x ) = ln | csc x + cot x | . Formula Used: Derivative of natural logarithm f ( x ) = ln ( x ) is f ′ ( x ) = 1 x . Derivative of ln u using chain rule is d d x ( ln u ) = d d x ( ln u ) ⋅ d u d x . Calculation: Consider the function z ( x ) = ln | csc x + cot x | . Represent the function in the form of d y d x . d d x ( ln | csc x + cot x | ) Then determine the derivative of natural logarithm and apply chain rule. d d x ( ln | csc x + cot x | ) = ( 1 csc x + cot x ) ⋅ d d x ( csc x + cot x ) Consider the expression d d x ( csc x + cot x )

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.2, Problem 32E

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To calculate: The derivative of the function z(x)=ln|cscx+cotx|.

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Chapter 9.2, Problem 31E

Chapter 9.2, Problem 33E

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Chapter 9 Solutions

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The derivative of the function z ( x ) = ln | csc x + cot x | .

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Chapter 9 Solutions