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