Implicit

187 days ago by night1394

 
       
Yvar=var('y') Yf=function('y',x) Expr=-x^2 +Yf^3-3*Yf^2+Yf+3*x-5 Deriv = diff(Expr) print("1.") solve(Deriv,diff(Yf)) 
        
1.
[D[0](y)(x) == (2*x - 3)/(3*y(x)^2 - 6*y(x) + 1)]
1.
[D[0](y)(x) == (2*x - 3)/(3*y(x)^2 - 6*y(x) + 1)]
Yvar=var('y') Yf=function('y',x) Expr=sin(x*Yf)-x^2+3*x Deriv = diff(Expr) print("2.") solve(Deriv,diff(Yf)) 
        
2.
[D[0](y)(x) == -(cos(x*y(x))*y(x) - 2*x + 3)/(x*cos(x*y(x)))]
2.
[D[0](y)(x) == -(cos(x*y(x))*y(x) - 2*x + 3)/(x*cos(x*y(x)))]
var('x,y,z') Expr=3*x^2*z-x^2*y^2+2*z^3+3*y*z-5 dx = diff(Expr,x) dy = diff(Expr,y) dz = diff(Expr,z) print("3.") print("dz/dx=") print(dx/dz) print("dz/dy=") print(dy/dz) 
        
3.
dz/dx=
-2/3*(x*y^2 - 3*x*z)/(x^2 + 2*z^2 + y)
dz/dy=
-1/3*(2*x^2*y - 3*z)/(x^2 + 2*z^2 + y)
3.
dz/dx=
-2/3*(x*y^2 - 3*x*z)/(x^2 + 2*z^2 + y)
dz/dy=
-1/3*(2*x^2*y - 3*z)/(x^2 + 2*z^2 + y)
var('x,y,z') Expr=sin(x*y)-z*x^2+e^(x*z) dx = diff(Expr,x) dy = diff(Expr,y) dz = diff(Expr,z) print("4.") print("dz/dx=") print(dx/dz) print("dz/dy=") print(dy/dz) 
        
4.
dz/dx=
(2*x*z - y*cos(x*y) - z*e^(x*z))/(x^2 - x*e^(x*z))
dz/dy=
-x*cos(x*y)/(x^2 - x*e^(x*z))
4.
dz/dx=
(2*x*z - y*cos(x*y) - z*e^(x*z))/(x^2 - x*e^(x*z))
dz/dy=
-x*cos(x*y)/(x^2 - x*e^(x*z))
var('x,y,z') Expr=cos(x+y)-sin(y+z) dx = diff(Expr,x) dy = diff(Expr,y) dz = diff(Expr,z) print("5.") print("dz/dx=") print(dx/dz) print("dz/dy=") print(dy/dz) print("dy/dx=") print(dx/dy) 
        
5.
dz/dx=
sin(x + y)/cos(y + z)
dz/dy=
(sin(x + y) + cos(y + z))/cos(y + z)
dy/dx=
sin(x + y)/(sin(x + y) + cos(y + z))
5.
dz/dx=
sin(x + y)/cos(y + z)
dz/dy=
(sin(x + y) + cos(y + z))/cos(y + z)
dy/dx=
sin(x + y)/(sin(x + y) + cos(y + z))