Explanation 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 . (5) The derivative of the logarithm function rule, d d x ( ln a x ) = 1 x . (6) The derivative of the exponential function rule, d d x ( e a x ) = 1 a e a x . Calculation: The given function is y = ( x 2 + 1 ) e 2 x ln x . Let y = f ( x ) , then f ( x ) = ( x 2 + 1 ) e 2 x ln x . The given function is in the quotient form. Apply the above mentioned formulas for the given function to obtain the derivative. Let u ( x ) = ( x 2 + 1 ) e 2 x and v ( x ) = ln x . d d x [ ( x 2 + 1 ) e 2 x ln x ] = ( ln x ) ⋅ d d x [ ( x 2 + 1 ) e 2 x ] − ( x 2 + 1 ) e 2 x ⋅ d d x ( ln x ) ( ln x ) 2 [ ∵ by Quoitent rule ] = ln x ⋅ [ e 2 x d d x ( x 2 + 1 ) + ( x 2 + 1 ) d d x ( e 2 x ) ] − ( x 2 + 1 ) e 2 x 1 x ( ln x ) 2 &#

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

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

Publisher: PEARSON

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Chapter 4, Problem 42RE

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To find: The derivative of the given function by the differential rules.

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Chapter 4, Problem 41RE

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Chapter 4 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

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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