evaluating derivative of implicit function

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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