Explanation Given function f x = e x 3 x + 2 can be derivated by the following rules. Rule for derivative of e g x : d e g x d x = e g x g ' x Based on the above mentioned rule, d e x 3 x + 2 d x = e x 3 x + 2 g ' x 3 x + 2 x 3 x + 2 can be written as, x 3 x + 2 = x 3 x + 2 1 2 Hence, g ' x 3 x + 2 = g ' x 3 x + 2 1 2 g ' x 3 x + 2 1 2 is determining using the following rule, 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 function times the derivative of the second plus the second function times the derivative of the first. Based on the above product rule, Let u ( x ) = x v ( x ) = 3 x + 2 1 2 According to constant times a function rule, power rule and Constant rule u ' x and v ' x are determined as below, u ' x = x 1 - 1 = 1 v ' x = 1 2 3 x + 2 1 2 - 1 3 v ' x = 3 2 3 x + 2 - 1 2 Substituting u ' x and v ' x and u ( x ) , v ( x ) in the below function, g ' x 3 x + 2 1 2 = u ( x ) · v ' x + v ( x ) · u ' x

2nd Edition

ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

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Chapter 4.4, Problem 33E

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The derivative of the function fx=ex3x+2.

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Chapter 4.4, Problem 32E

Chapter 4.4, Problem 34E

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Chapter 4 Solutions

Calculus For The Life Sciences

Ch. 4.1 - YOUR TURN If ft=1t, find f't.Ch. 4.1 - Prob. 2YT Ch. 4.1 - YOUR TURN If ht=-3t2+2t+5t4-7, find h't.Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...

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