Is there any sensible definition of a something like a “half” derivative, or more generally an nth derivative for a non-integer n? Strictly speaking, the derivative only makes sense in integer increments. The “2nd derivative” is the derivative of the derivative, and it tells you how fast the slope is changing. For all natural numbers N, N! Finally, and this is very round-about, but it turns out that a really good way to do half a derivative is to do half an integral and then do a full derivative of the result:That “root pi” is just another math thing.