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# Lista de exercícios Introdução Derivada Parcial

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```GRADUAÇÃO
CURSO: ENGENHARIAS
DISCIPLINA: Cálculo Diferencial e Integral II

Lista \u2013 Introdução a Derivadas Parciais

e \ud835\udc53!; e para \ud835\udc53 \ud835\udc65,\ud835\udc66, \ud835\udc67 : \ud835\udc53!, \ud835\udc53! e \ud835\udc53!.

a) f (x, y) = 6x +3y \u22127 b) f (x, y) = 4x2 \u22123xy
c) f (x, y) = 3xy +6x \u2212 y2 d ) f (x, y) = xy2 \u22125y +6
e) f (x, y) = x2 + y2 f ) f (x, y) = x + 2y
x2 \u2212 y
g) f (x, y, z) = x2 y \u22123xy2 + 2yz h) f (x, y, z) = 4xyz + ln (2xyz)
i) f (x, y, z) = (x2 + y2 + z2 )
\u22121
2 j) f (x, y, z) = exy . sen (2z)\u2212 exz
l) f (x, y, z) = exyz + sen( 3xy
z2
) m) f (x, y, z) = cos (xyz)

a) f (\u3b8 ,\u3d5 ) = sen 3\u3b8. cos2\u3d5 , f\u3b8 e f\u3d5
b) f (r,\u3b8 ) = r2 cos \u3b8 \u2212 2r.tg\u3b8 , fr e f\u3b8
c) f (r,\u3b8 ,\u3d5 ) = 4r2 sen \u3b8 +5er cos \u3b8.sen \u3d5 \u2212 2cos \u3d5 , fr , f\u3b8 e f\u3d5
d ) f (r,\u3b8 ) = r tg\u3b8 \u2212 r2sen\u3b8 , fr 2,
\u3c0
4
&quot;
#
\$
%
&
'
e) f (x, y, z) = exy
2
+ ln (y + z), f x (3,0,17), f y (1,0,2) e fz (0,0,1)

f) \ud835\udc53 \ud835\udc65,\ud835\udc66 = ln \ud835\udc65 + \ud835\udc65! + \ud835\udc66! , \ud835\udc53!(3,4)
g) \ud835\udc53 \ud835\udc65,\ud835\udc66, \ud835\udc67 = \ud835\udc60\ud835\udc52\ud835\udc5b!\ud835\udc65 + \ud835\udc60\ud835\udc52\ud835\udc5b!\ud835\udc66 + \ud835\udc60\ud835\udc52\ud835\udc5b!\ud835\udc67, \ud835\udc53!(0,0,4)

3 - Dada a função \ud835\udc64 = \ud835\udc53(\ud835\udc65,\ud835\udc66, \ud835\udc67), mostre que a igualdade é válida.

w = x2 y + y2z + z2x; \u2202w
\u2202x
+
\u2202w
\ufffd\ufffd\ufffdy
+
\u2202w
\u2202z
= (x + y + z)2```