From my daughter’s region test practice set of problems, there is this one:

First try to figure out what the right part is, assuming x^3 same as e is an irrelevant variable.

The key here is using the origin function, substituting the part that is being deducted as a constant. Then apply the derivative dx again. It becomes

To calculate this derivative of a function, we just need to apply the chain rule: F'(g(x)) =

Plug in back to get

If you try to solve this problem by plugging in basic bricks such as

It goes to haywire but definitely solvable. (need to complete later)

citing important formulas:

On Feb 2025, ask AI to deduce this Leibniz rule: