# evaluating derivative of implicit function

I am trying to evaluate the derivative of an implicitly defined function

rho = function('rho',u)
u_z_equation = u*z^3 - u*z^2 - z^3 + z^2 - 2*z + 1
implicit = u_z_equation(z=rho)
rho_1 = solve(implicit(u=1),rho(1))[0]
print rho_1
d_rho = solve(diff(implicit,u),diff(rho))[0]
print d_rho(u=1)


But I do not know how to substitute the value I found for rho(1) into the expression for the derivative

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You can do it like this (subs accepts relational arguments):

d_rho(u=1).subs(rho_1)

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thanks rburing

( 2019-04-06 07:23:50 -0500 )edit

You're welcome. You can also vote up and accept the answer using the buttons on the left of it.

( 2019-04-06 08:03:25 -0500 )edit

@rburing: it's also important to upvote questions that are good enough to deserve an answer, especially questions by users with low karma; users with low karma can only accept anwers but cannot upvote!

( 2019-04-08 16:39:41 -0500 )edit