Comment #48 on issue 1816 by asmeurer: Adding partial derivatives and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
Or in concrete terms, why is it that diff(expr, cos(2*x)) works but diff(expr, 2*cos(x)) raises?
Because cos(2*x) can unambiguously be replaced in the original expression with the simple rule of "exact" substitution like discussed on the list.
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