Sheet (5) solution - 1 Math 103 Class Work Sheet (5)...

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Unformatted text preview: 1 Math 103 Class Work Sheet (5) Solution [1] (a) x x x e x xe y e x y 2 2 2 ' (b) 2 2 ) 1 ( ) 1 ( ) 1 ( ' 1 x xe x e e x y x e y x x x x (c) ) 9 .( ' 2 3 3 3 3 x e y e y x x (d) ) 2 (cos ) 2 sin ( ' ) 2 (cos x x e x e y x x e y x x x (e) ) 3 ).( 2 .( 2 1 2 1 ' 2 1 3 3 3 x x x e e y e y (f) ) 2 ).( )).( sin( .( ) cos( ' ) cos( 2 2 2 2 x x x x e e x e y e x y (g) 2 ) ln 1 ( 1 ). 1 ( ) ).( ln 1 ( ' ln 1 1 x x e e x y x e y x x x (h) x x x x e e x e y e x y 1 . ) 1 ln( ' ) 1 ln( (i) x x y x x y 1 1 1 ' ln sin 2 1 (j) ) 2 .( 1 2 1 1 . 1 1 ' ) 1 ln( 2 2 2 x x x x y x x y (k) 2 ) 2 3 ( ) 3 )( 2 3 ( ) 3 )( 2 3 ( . 2 3 2 3 2 1 ' 2 3 2 3 x x x x x y x x y Or 2 3 3 2 3 3 2 1 ' ) 2 3 ln( ) 2 3 ln( 2 1 ln 2 3 2 3 ln ln x x y y x x y x x y 2 3 3 2 3 3 2 3 2 3 2 1 2 3 3 2 3 3 2 1 . ' x x x x x x y y (l) 3 24 1 2 10 ) 3 ( ) 1 2 ( 3 24 1 2 10 ' ) 3 ln( 6 ) 1 2 ln( 5 ln ) 3 ( ) 1 2 ( 4 3 6 4 5 4 3 4 6 4 5 x x x x x y x x x y y x x y x x y (m) 1 20 2 2 1 . ) 1 ( ' ) 1 ln( 10 ln 2 1 ln ) 1 ( 2 10 2 2 2 10 2 2 2 x x x x x e x y x x x y x e x y x x 2 (n) ) 2 ).( 3 ln 3 ).( 2 ).(ln 2 ( ' 2 ln . 3 ln 2 2 2 2 2 3 3 x y y y x x x x (o) 2 1 1 1 ). 5 .(ln 5 ' 5 x y y x x (p) x x x y x y 1 . ) ln( 1 . )) ln(ln( 1 ' ))) ln(ln(ln( (q) 1 4 tan sec 4 sin cos 2 . ) 1 ( tan sin ' ) 1 ln( 2 ) ln(tan 4 ) ln(sin 2 ln ) 1 ( tan sin 2 2 2 2 4 2 2 2 2 4 2 x x x x x x x x x y x x x y x x x y (r) x x x x x y x x y x y x x sin cos ) ln(sin . ) (sin ' ) ln(sin ln ) (sin (s) x x x y x x x y x y x x ln 2 . ' ) (ln ln . ln ln ln 2 ln (t) x x x x x x y x x y x y x x ln cos ) ln(ln . sin . ) (ln ' ) ln(ln . cos ln ) (ln cos cos (u) ) 1 ( 2 sin cos 1 . 1 sin 2 1 ' ) 1 ln( 2 1 ) ln(sin ln 2 1 ln 1 sin x x x x x e e x x x e x y e x x y e x x y (v) ) 6 ln( 4 1 ) 2 ln( 2 1 ) 1 ln( 3 ln 6 2 ) 1...
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This note was uploaded on 01/09/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Spring '09 term at German University in Cairo.

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Sheet (5) solution - 1 Math 103 Class Work Sheet (5)...

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