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> The natural logarithm being its own derivative

the derivative of ln(x) is 1/x

> the derivative a radians-based sin(x) being cos(x) and so on. Make it any other unit, and you have a mess of conversion factors worse than 2pi.

the derivative (with respect to x) of sin(x) is cos(x), regardless of units for x. Otherwise the chain rule wouldn't work

> the derivative (with respect to x) of sin(x) is cos(x), regardless of units for x.

Not if you use "turn"-trigonometric functions, as the author suggests.

turn-sin `t sin(x) = sin(2pi * x)` has `d/dx tsin(x) = 2pi * tcos(x)`.

such a weird thread because everyone seems to know what they are talking about but definitely seem to miss something.

but basically one would be differentiating to 2pi x rather than x. and things will work out