To determine To find: The derivative of the given function using the quotient rule . Explanation Given: The function is f ( t ) = 4 t 2 + 11 t 2 + 3 . Formula used: (1). The quotient rule is, d d x [ u ( x ) v ( x ) ] = v ( x ) ⋅ u ' ( x ) − u ( x ) ⋅ v ' ( x ) ( v ( x ) ) 2 . (2). The sum or difference rule , d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) . (3) The power rule, d d x ( x n ) = n x n − 1 . (4) The constant rule, d d x ( k ) = 0 . Calculation: The given function is in the quotient form. Apply the quotient rule for the given function. Let u ( t ) = 4 t 2 + 11 and v ( t ) = t 2 + 3 . d d t [ 4 t 2 + 11 t 2 + 3 ] = ( t 2 + 3 ) ⋅ d d t ( 4 t 2 + 11 ) − ( 4 t 2 + 11 ) ⋅ d d t ( t 2 + 3 ) ( t 2 + 3 ) 2 = ( t 2 + 3 ) ( d d t ( 4 t 2 ) + d d t ( 11 ) ) − ( 4 t 2 + 11 ) ( d d t ( t 2 ) + d d t ( 3 ) ) ( t 2 + 3 ) 2 x

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

Author: Margaret L. Lial; Nathan P. Ritchey; Raymond N. Greenwell

Publisher: Pearson Education

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Chapter 4.2, Problem 17E

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To find: The derivative of the given function using the quotient rule.

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Chapter 4.2, Problem 16E

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Chapter 4 Solutions

Calculus with Applications Books a la Carte Edition

Ch. 4.1 - YOUR TURN 1 find f′(t). Ch. 4.1 - YOUR TURN 2 find dy/dx. Ch. 4.1 - Prob. 3YT Ch. 4.1 - Prob. 4YT Ch. 4.1 - Prob. 5YT Ch. 4.1 - Prob. 1WE Ch. 4.1 - Prob. 2WE 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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