Lista 1 - Sistemas Lineares

Derivadas parciais

1)f(x,y)=2x^2-3y-4dx=4x, dy=-32) f(x,y)=x^2-xy+y^2dx= 2x-y, dy= -x+2y3) f(x,y)=(x^2-1)*(y+2)

dx=2x(y+2) , dy=x^2-14) f(x,y)=5xy-7x^2-y^2+3x-6y+2dx= 5y-14x+3 , dy=5x-2y-65) f(x,y)=(xy-1)^2dx= 2y(xy-1) , dy=2x(xy-1)

6) f(x,y)=(2x-3y)^3dx= 6(2x-3y)^2 , dy=-9(2x-3y)^27) f(x,y)=raiz(x^2+y^2)dx=x/raiz (x^2+y^2) , dy=y/raiz (x^2+y^2)

8) f(x,y)=(x^3+(y/2))^2/3dx= 2x^2/ raiz cubica (x^3 + (y/2)) , dy=1/ raiz cubica (x^3 + (y/2))

9) f(x,y)=1/(x=y)dx=1/(x+y)^2 , dy= 1/(x+y)^2 10) f(x,y)=x/(x^2 + y^2)

dx=y^2-x^2/(x^2+y^2)^2 , dy= 2xy / (x^2+y^2)^

11) f(x,y)=(x+y)/(xy-1)

Dx= -y^2-1 / (xy-1)^2 , Dy= -x^2-1 / (xy-1)^2

13) f(x,y)=e^(x+y+1)

Dx= e^(x+y+1) , Dy= e^(x+y+1) 14) f(x,y)=e^(-x)* sen(x+y)

Dx= e^(-x)* sen(x+y)+ e^(-x)* cos(x+y) dy= e^(-x)* cos(x+y)

15) f(x,y)=ln(x+y)

Dx=1/x+y , Dx=1/x+y

16) f(x,y)=e^(xy)*ln(y)

Dx=y e^(xy)*ln(y) , Dx=xe^(xy)*ln(y)+(e^(xy)/y)17) f(x,y)=sen^2(x-3y)

Dx= 2sen(x-3y)*cos(x-3y) , Dx= -6sen(x-3y)*cos(x-3y)

18) f(x,y)=cos^2(3x-y^2)

Dx= -6cos(3x-y^2)*sin(3x-y^2) , dy= Dx= 4ycos(3x-y^2)*sin(3x-y^2)

19) f(x,y)=x^y

Dx= yx^(y-1) , Dy= x^y*lnx

Derivadas parciais fx,fy e fz25)F(x,y,z)=x-raiz(y^2 + z^2)

Fx=1, Fy= - y / (raiz(y^2 + z^2) , Fz= - z / raiz(y^2 + z^2)

26) F(x,y,z)=(x^2+y^2+z^2)^-1/2Fx=-x(x^2+y^2+z^2)^-3/2, Fy= -y(x^2+y^2+z^2)^-3/2, Fz= -z(x^2+y^2+z^2)^-3/2, 29) F(x,y,z)=ln(x+2y+3z)Fx= 1/ (x+2y+3z) , Fy= 2/ (x+2y+3z) , Fz= 3/ (x+2y+3z)

30) F(x,y,z)=yz * ln(xy)Fx=yz/x , Fy=z ln(xy) , Fz=y ln (xy)31) F(x,y,z)=e^-(x^2+y^2+z^2)

Fx=-2x e^-(x^2+y^2+z^2) , Fy=-2y e^-(x^2+y^2+z^2) , Fz=-2z e^-(x^2+y^2+z^2)

32) F(x,y,z)=e^(-xyz)Fx=-yz e^(-xyz) , Fy=-xz e^(-xyz) , Fz=-xy e^(-xyz)