ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 25 Apr 2020 02:54:34 -0500Formal implicit differentiationhttps://ask.sagemath.org/question/50991/formal-implicit-differentiation/As my question was poorly asked, I rewrite it.
I was searching for the code of first order and second order differentiation of an implicit function. Finally I found and post it.Fri, 24 Apr 2020 11:41:04 -0500https://ask.sagemath.org/question/50991/formal-implicit-differentiation/Answer by Cyrille for <p>As my question was poorly asked, I rewrite it.</p>
<p>I was searching for the code of first order and second order differentiation of an implicit function. Finally I found and post it.</p>
https://ask.sagemath.org/question/50991/formal-implicit-differentiation/?answer=50999#post-id-50999Here is the code for first and second order implicit differentiation of a two variables function
#Evaluation of the two first derivatives of an implicit function
var("x, y, dx, dy, al, be")
V=function('V')(x, y)# A) either A or B should be uncomment
#V= x^al*y^be# B)
V_x = diff(V, x)
V_y = diff(V, y)
#Evaluation of the two first derivatives of an implicit function
var("x, y, dx, dy, al, be")
V=function('V')(x, y)# A) either A or B should be uncomment
#V= x^al*y^be# B)
V_x = diff(V, x)
V_y = diff(V, y)
# Differential
dV = V_x * dx + V_y * dy
show(dV)
# Dérivée du premier ordre
sol=solve(dV==0, dy)
show(sol[0]/dx)
# Dérivée du second ordre
y_x=sol[0].rhs()/dx
show(y_x)
hh=y_x.function(x,y)
y=function('y')(x)
hh_x=diff(hh(x,y),x).full_simplify().subs(diff(y(x), x)==y_x).full_simplify()
show(hh)
show(hh_x)
$\frac{\mathit{dy}}{\mathit{dx}} = -\frac{\frac{\partial}{\partial x}V\left(x, y\right)}{\frac{\partial}{\partial y}V\left(x, y\right)}$
$-\frac{\frac{\partial}{\partial x}V\left(x, y\right)}{\frac{\partial}{\partial y}V\left(x, y\right)}$
Now I will work on the substitution of the chosen function. And when I will have found I will come back.Sat, 25 Apr 2020 02:54:34 -0500https://ask.sagemath.org/question/50991/formal-implicit-differentiation/?answer=50999#post-id-50999