Implicit diff

189 days ago by potato

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