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Homework4 - MA 115 Homework Solutions for Week 4 3.5 #2 Let...

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Unformatted text preview: MA 115 Homework Solutions for Week 4 3.5 #2 Let u = g ( x ) = 4 + 3 x and y = f ( u ) = √ u = u 1 / 2 . Then dy dx = dy du du dx = 1 2 u − 1 / 2 (3) = 3 2 √ u = 3 2 √ 4+3 x . 3.5 #6 Let u = g ( x ) = e x and y = f ( u ) = sin u . Then dy dx = dy du du dx = (cos u )( e x ) = e x cos e x . 3.5 #18 h ( t ) = ( t 4- 1) 3 ( t 3 + 1) 4 ⇒ h ′ ( t ) = ( t 4- 1) 3 · 4( t 3 + 1) 3 (3 t 2 ) + ( t 3 + 1) 4 · 3( t 4- 1) 2 (4 t 3 ) = 12 t 2 ( t 4- 1) 2 ( t 3 + 1) 3 bracketleftbig ( t 4- 1) + t ( t 3 + 1) bracketrightbig = 12 t 2 ( t 4- 1) 2 ( t 3 + 1) 3 (2 t 4 + t- 1) 3.5 #31 y = sin parenleftBig tan √ sin x parenrightBig ⇒ y ′ = cos parenleftBig tan √ sin x parenrightBig · d dx parenleftBig tan √ sin x parenrightBig = cos parenleftBig tan √ sin x parenrightBig sec 2 √ sin x · d dx (sin x ) 1 / 2 = cos parenleftBig tan √ sin x parenrightBig sec 2 √ sin x · 1 2 (sin x ) − 1 / 2 · cos x = cos parenleftBig tan √ sin x parenrightBigparenleftBig sec 2 √ sin x parenrightBig...
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This note was uploaded on 04/07/2008 for the course MA 115 taught by Professor Mahalanobis during the Fall '08 term at Stevens.

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Homework4 - MA 115 Homework Solutions for Week 4 3.5 #2 Let...

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