*-tarea 3-*

1) Calcular el gradiente de la funcion:

a)f(x,y) =

4X2-3Y2+Y2
f"(X)= (8x-3y) if"(Y)= (-3x+2y)jVf(x,y)= (8x-3y) i - (-3x+2y)j

b)f(x,y,z)=

f"(X)= (x+z)(1)-(x-y)(1)/(x+z)2= (x+z)-(x-y)/(x+z)2= i
f"(Y)= (x+z)(-1) - (y)(0)/(x+z)2= -x+z/(x+z)2= j
f"(Z)= (x+z)(0)-(x-y)(1)/(x+z)2= k

Vf(x,y,z) =
(z+y/(x+z)2) i (-1/x+z )j (-x+y/(x+z)2)K

2) Calcular la Divergencia y el Rotacional del campo Vectorial f:
a)f(x,y,z)=
6X2 i - XY2 j
div f(x,y,z) = 6X2 i - XY2 j= 12x-x2y


((-x2y )(0)- (-x)(0)) i- ((12x)(0)-( 6)(0)) j+ ((12x)(-x)-( 6)(-x2y ))k= 0i +0j+ (12+62Y)
= 0i +oj - 12+62Y


b)



div. f (x,y,z)= sen x i+ cos y j +Z2 k= cos x i - sen y j + 2 z k


((-seny )()-(cosy)(2z)) i - ((cosx)()-(senx)(2z))j
+ ((cosx)(cosy)-(senx)(-seny))k= ((-seny-cosy2z) i - (cosx-senx2z) j+ (cosxcosy-senx+seny) k
c)



((0)) i - ((0))j+ (( )()- ()(0)) k