Explanation Given expression y = x + 1 x + 2 can be derivated by the following rules, Where, x can be written as x = x 1 2 . Substituting x = x 1 2 in the given expression, y = x + 1 ( x ) 1 2 + 2 Definition of the Product Rule: If f ( x ) = u ( x ) · v ( x ) , and if u ' x and v ' x both exist, then f ' x = u ( x ) · v ' x + v ( x ) · u ' x . The derivative of a product of two functions is the first functions times the derivative of the second plus the second function times the derivative of the first. Based on the above product rule, Let us consider f ( x ) = y u ( x ) = ( x + 1 ) v ( x ) = ( x ) 1 2 + 2 Then, f ' x = y ' According to the Power Rule and Constant Rule, u ' x and v ' x can be written as below, u ' x = x 1 - 1 + 0 u ' x = x 0 + 0 u ' x = 1 Similarly, v ' x = 1 2 ( x ) 1 2 - 1 + 0 v ' x = 1 2 ( x ) - 1 2 Substituting f ' x = y ' , u ' x = 1 , v ' x = 1 2 ( x ) - 1 2 , u ( x ) = ( x + 1 ) and v ( x ) = ( x ) 1 2 + 2 in the below function, f ' x = u ( x ) · v ' x + v ( x ) · u ' x . y ' = ( x + 1 ) · 1 2 ( x ) - 1 2 + ( x ) 1 2 + 2 · 1

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 4.2, Problem 7E

To determine

To find:

The derivative of the expression y=x+1x+2, using the product rule.

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Chapter 4.2, Problem 6E

Chapter 4.2, Problem 8E

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