Explanation Formula used: d d x ( x n ) = n x n − 1 d d x ( ln x ) = 1 x d d x ( a f ( x ) + b g ( x ) ) = a d d x ( f ( x ) ) + b d d x ( g ( x ) ) d d x f ( g ( x ) ) = f ′ g ( x ) ⋅ g ′ ( x ) Calculations: Consider the function, y = e 3 x 2 ( x 3 + 1 ) 2 ( 4 x − 7 ) − 2 Take natural log on both sides, ln ( y ) = ln ( e 3 x 2 ( x 3 + 1 ) 2 ( 4 x − 7 ) − 2 ) = ln ( e 3 x 2 ) − ln ( ( x 3 + 1 ) 2 ( 4 x − 7 ) − 2 ) [ ∵ ln ( a b ) = ln a − ln b ] = ln ( e 3 x 2 ) − [ ln ( x 3 + 1 ) 2 + ln ( 4 x − 7 ) − 2 ] [ ∵ ln ( a b ) = ln a + ln b ] = ln ( e 3 x 2 ) − ln ( x 3 + 1 ) 2 − ln ( 4 x − 7 ) − 2 = 3 x 2 ln ( e ) − 2 ln ( x 3 + 1 ) + 2 ln ( 4 x − 7 ) [ ∵ ln ( a b ) = b ln a ] = 3 x 2 + 2 ln ( 4 x − 7 ) − 2 ln ( x 3 + 1 ) [ ∵ ln ( e ) = 1 ] Now, differentiate both sides of the above equation, d d x ( ln y ) = d d x ( 3 x 2 + 2 ln ( 4 x − 7 ) − 2 ln ( x 3 + 1 ) ) 1 y d y <

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.6, Problem 44PS

To determine

To find:the derivatives of the function y=e3x2( x 3 +1)2( 4x−7)−2 .

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Chapter 3.6, Problem 43PS

Chapter 3.6, Problem 45PS

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Chapter 3 Solutions

Calculus

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the derivatives of the function y = e 3 x 2 ( x 3 + 1 ) 2 ( 4 x − 7 ) − 2 .

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To find:the derivatives of the function y=e3x2( x 3 +1)2( 4x−7)−2 .

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Chapter 3 Solutions