gma00108-lista-11 - LISTA DE EXERC ICIOS DEPARTAMENTO DE...

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GMA DEPARTAMENTO DE MATEMÁTICA APLICADA GM LISTA DE EXERC ´ ICIOS alculo I –A– Humberto Jos´ e Bortolossi http://www.professores.uF.br/hjbortol/ 11 A regra da cadeia [01] Derive cada uma das fun¸ oes dadas abaixo. (a) F ( x )=( x 3 +4 x ) 7 ,( b ) F ( x x 2 x +1) 3 , (c) F ( x )= 4 1+2 x + x 3 , (d) f ( x )=(1+ x 4 ) 2 / 3 , (e) g ( t )=1 / ( t 4 3 , (f) f ( t 3 p 1+tg( t ), (g) y =cos( a 3 + x 3 ), (h) y = a 3 +cos 3 ( x ), (i) y = e mx , (j) y =4sec(5 x ), (k) g ( x )=(1+4 x ) 5 (3 + x x 2 ) 8 l ) h ( t t 4 1) 3 ( t 3 4 , (m) y =(2 x 5) 4 (8 x 2 5) 3 , (n) y =( x 2 +1)( x 2 +2) 1 / 3 , (o) y = xe ( x 2 ) , (p) y = e 5 x cos(3 x ), (q) y = e x cos( x ) , (r) y =10 1 x 2 . (s) y =tg(cos( x )), (t) y =sen 2 ( x ) / cos( x ), (u) y =2 sen( πx ) , (v) y =tg 2 (3 θ ), (w) y = x x , (x) y = x sen( x ) , (y) y = sen(sen(sen( x ))), (z) y = sen(tg( p sen( x ))). [02] Derive cada uma das fun¸ oes dadas abaixo. y = r r 2 +1 b ) G ( y ( y 1) 4 ( y 2 +2 y ) 5 , F ( z r z 1 z d ) y = e 2 u e u + e u , y = q x + x , y = r x + q x + x . [03] Encontre todos os pontos sobre o gr´ aFco da fun¸c˜ ao f ( x )=2sen( x )+sen 2 ( x ) nos quais a reta tangente ´ e horizontal [04] A tabela abaixo apresenta valores para f , g , f 0 e
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gma00108-lista-11 - LISTA DE EXERC ICIOS DEPARTAMENTO DE...

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