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#                          FÍSICA COMPUTACIONAL II                           #
#                                   por                                      #
#                         Francisco  Carlos  Lavarda                         #
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                        LISTA DE EXERCÍCIOS DE 
                     DERIVADAS PARCIAIS E TOTAIS

Para cada uma das funções abaixo, calcule todas as derivadas parciais solicitadas e a derivada total:

[1] f(x,y)=4(x**2)(y**3)

    ordens: x:1, y:3: resp = 48*x
    total: 12*x^2*y^2*del(y)+8*x*y^3*del(x)


[2] f(x,y,z)=4(x**2)(y**3)sen(xyz)

    ordens: x:1, y:2, z=3; resp = -4*x^7*y^7*z^3*sin(x*y*z)+408*x^5*y^5*z*sin(x*y*z)+76*x^6*y^6*z^2*cos(x*y*z)-600*x^4*y^4*cos(x*y*z)
    total: 4*x^3*y^4*cos(x*y*z)*del(z)+(12*x^2*y^2*sin(x*y*z)+4*x^3*y^3*z*cos(x*y*z))*del(y)+(8*x*y^3*sin(x*y*z)+4*x^2*y^4*z*cos(x*y*z))*del(x)


[3] f(t,y,u)=t^5+((t+1)/t^2)*sen(2y)*cos(u)

    ordens: t:2, y:2, u:2 : resp = (24*(t+1)*cos(u)*sin(2*y))/t^4-(16*cos(u)*sin(2*y))/t^3
    total: (2*(t+1)*cos(u)*cos(2*y)*del(y))/t^2-((t+1)*sin(u)*sin(2*y)*del(u))/t^2+(-(2*(t+1)*cos(u)*sin(2*y))/t^3+(cos(u)*sin(2*y))/t^2+5*t^4)*del(t)


[4] g(a,b,c)=ln(a)*sen(b)*c**4

    ordens: a:1, b:2, c:3: resp = -(24*sin(b)*c)/a
    total: 4*log(a)*sin(b)*c^3*del(c)+log(a)*cos(b)*c^4*del(b)+(sin(b)*c^4*del(a))/a


[5] h(d,f,g)=e^(3*d^2+f+2g)

    ordens: d:1, f:2,  g:1: resp = 12*d*%e^(2*g+f+3*d^2)
    total: 2*%e^(2*g+f+3*d^2)*del(g)+%e^(2*g+f+3*d^2)*del(f)+6*d*%e^(2*g+f+3*d^2)*del(d)