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(d/dx) cos( pi ) = -sin( pi ) ... [You may need to think about this one]
@ColinTheMathmo not surprising, in instrumentation and design - this 90 degree phase shift is bread and butter. = 90 degree lead for differentiation (and inversely 90 degree lag for integration).
@markofmarks Are you sure you've read this correctly?
"pi" is not a variable ...
@ColinTheMathmo yes missed the twist in the tale.
However, of course d/dx of a constant will always be equal to zero as there is no rate of change, so the potential paradox is avoided (as sin(pi) is of course zero s well.