Differentiation

My math program can now symbolically compute the derivative of an expression.

Challenges

One tricky case was finding the derivative of x^x. Since x^x = e^(x*ln(x)), rewriting it in that form let the existing exponential and product rules handle it correctly.

Restrictions

Differentiation works well, but outputs aren’t always in the simplest form. Differentiating (x^2)/2, for instance, currently gives 0.5*2*x instead of the simplified x. Simplifying this is a lot harder than it looks at first because it is really hard to determine whether an action results in a simpler form or not.

Next up

I’ll pause the AST experiments here for now. There’s a lot more that could be done, but I want to make it demoable. Next step: a small web UI so people can try it out directly.