Explanation Given: The function, f ( t ) = 2 t 2 + t . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 Power rule of derivatives: d d x ( x n ) = n x n − 1 Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions 2 t and ( 2 + t ) . So, using the quotient rule and power rule of derivatives, it gives f ' ( t ) = d d t ( 2 t 2 + t ) = ( 2 + t ) ⋅ d d t ( 2 t )

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 29E

To determine

The derivative of the function, f(t)=2t2+t .

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Chapter 3.4, Problem 28E

Chapter 3.4, Problem 30E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

The derivative of the function, f ( t ) = 2 t 2 + t .

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

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The derivative of the function, f(t)=2t2+t .

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Chapter 3 Solutions