By differentiating a function at 0, I got the following equation in Sage.

(b - f(0))*(c - f(0))*D[0](f)(0) - 1 == 0

How do I make Sage

1. Plug in f(0) = b+c

2. Simplify and solve for D[0](f)(0)?

I tried

equation = (b - f(0))*(c - f(0))*D[0](f)(0) - 1 == 0
new_equation = equation.subs({f(0): b+c})
solve(new_equation, D[0](f)(0))

I get the following error

Substitution using function-call syntax and unnamed arguments has been removed. You can use named arguments instead, like EXPR(x=..., y=...)