A while back I realised you could do a similar thing by just working out the nth derivative analytically and chucking a real number in. For example, the nth der

A while back I realised you could do a similar thing by just working out the nth derivative analytically and chucking a real number in. For example, the nth derivative of x^m is (x^(m - n) m!)/(m - n)! You can gradually vary n from 0 to 1 to see the smooth change. It doesn't always behave how you'd expect it to. Same for e^ix: i^n e^(i x) Which means you can partially differentiate sin, cos etc. (In fact, the power derivative lets you derive any function via its taylor series). What do you think the gradient of sin looks like if you take it gradually and animate it? You might expect it to slowly move to the left and become cos. It does, but it also does a barrel roll around the real axis at the same time. Kinda neat – I wish there was an easy way to put a demo up. I tried to figure out some physical applications for this but I've fallen short so far – would be interested to know if there are any.