Scientific Notebook handles implicit differentiation in a natural way.
You can use Define + New Definition to declare a character to be a (generic) constant.
Define + New Definition
a
Calculus + Implicit Differentiation
ax + y = 0 (Differentiation Variable: x) Derivative: a + y′ = 0
bx + y = 0 (Differentiation Variable: x) Derivative: b′x + b + y′ = 0
Note that a′ = 0 while b′ is not automatically assumed to be 0.