Graphing derivatives of implicitly given functions

Surely there is a way to do this numerically, isn't there? What I mean is that one should be able to write a function which, for a given numerical value of x, solves the implicit equation to find the value of the derivative at x -- using find_root, perhaps. And then one ought to be able to plot this function.

Of course this won't work for every implicitly defined function, but sage's numerics should work for a lot of cases that users actually want.

But I don't know enough about sage symbolics to actually do this. Any takers?

You can try this:

y=function('y',x) 
var('x,yy,z')
f=x*y+x^2-y^3*x
ff=f.diff(x).subs({y.diff(x):z,y:yy})
implicit_plot3d(ff,(x,-3,3),(yy,-3,3),(z,-4,4))

This way you avoid the "solve" issue.

I am not sure whether this is what you are looking for

y(x)=sin(x)
plot(diff(sin(x),x),(x,0,pi))