Set the order to five and the calculator differentiates five times, simplifying between rounds. Two things happen that are worth watching.
Expressions grow, then sometimes shrink
A product like x³ sin x grows quickly: each round applies the product rule and doubles the term count
before simplification pulls it back. By the fifth derivative there are dozens of steps. Trigonometric
functions alone behave differently — sin x cycles back to itself every four rounds, so its higher
derivatives never grow at all.
The working needs paging
A fifth-order derivative can run past a hundred recorded steps. Writing all of them at once costs a typeset pass per step and makes the page crawl, so the steps are written out in batches with a button for the rest. Nothing is discarded — the earlier version of this site silently truncated at forty, which was worse than useless because it looked complete.