Explanation Given information: v = 2 t 2 + 1 t + 1 Formula used: 1) Constant –multiple rule: d d x [ k ⋅ f ( x ) ] = k ⋅ d d x [ f ( x ) ] , k is a constant 2) General Power rule: d d x ( [ g ( x ) ] r ) = r ⋅ [ g ( x ) ] r − 1 ⋅ d d x g ( x ) 3) Sum rule : d d x [ f ( x ) + g ( x ) ] = d d x [ f ( x ) ] + d d x [ g ( x ) ] 4) Derivative of a constant: d d x [ C ] = 0 , C is a constant. 5) Power rule: d d x ( x r ) = r ⋅ x r − 1 6) To obtain f ' ( x ) differentiate a function f ( x ) . f ' ( x ) is the slope of the curve y = f ( x ) . To obtain f ' ' ( x ) differentiae the function f ' ( x ) that is d d x f ' ( x ) = f ' ' ( x ) . Calculation: The function v = 2 t 2 + 1 t + 1 can be written as v = 2 t 2 + ( t + 1 ) − 1 . To compute d d t ( d v d t ) , we first need to calculate d v d t . d v d t = d d t [ 2 t 2 + ( t + 1 ) − 1 ] By using the sum rule, = d d t ( 2 t 2 ) + d d t ( t + 1 ) − 1 By using the constant multiple rule of a derivative and the general power rule, = 2 d d t ( t 2 ) + [ − 1 ⋅ ( t + 1 ) − 2 ⋅ d d t ( t + 1 ) ] By using the sum rule, = 2 d d t ( t 2 ) − 1 ⋅ ( t

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Author: Asmar

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Chapter 1.7, Problem 30E

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To calculate: ddt ( dvdt ) where v = 2t2 + 1t + 1

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Chapter 1.7, Problem 29E

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Chapter 1 Solutions

EBK CALCULUS & ITS APPLICATIONS

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d d t ( d v d t ) where v = 2 t 2 + 1 t + 1

Solution Summary: The author explains that k is a constant.

To calculate: ddt ( dvdt ) where v = 2t2 + 1t + 1

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Chapter 1 Solutions