# sim-lib-numbers-cas-diff
In one line: It does calculus on your formulas, finding derivatives and integrals as tidy new expressions.
## What it gives you
Give it a formula and ask for the derivative, and it hands back the answer as a clean formula you can read, reuse, and simplify further. It also works the other way, finding integrals symbolically. This is the calculus you remember from school, done automatically and exactly on the algebraic form rather than on approximate numbers. Because the set of rules it follows can be extended, you or the system can teach it how to differentiate new operations, and it will apply them wherever they appear. The result is real, symbolic calculus you can trust rather than a numerical guess.
## Why you will be glad
- Derivatives and integrals come back as exact formulas, not rounded estimates.
- You get schoolbook calculus done instantly and without arithmetic slips.
- New operations can be taught once and then handled everywhere automatically.
## Where it fits
This is the calculus layer atop the SIM computer-algebra system. It takes the symbolic expressions defined by the core algebra crate and transforms them, giving the constellation the ability to reason about change and accumulation at the formula level.