That is actually fairly common notation in fractional calculus, where we in fact can work with (d/dx)^alpha where alpha can be many things that aren't necessarily integer. 
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Do you recommend any textbooks on fractional calculus?
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If you write dx/d instead of (d/dx)^-1 it works out perfectly lol
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hahaha I was thinking of that same thing! but I decided against it, because it's not conventional.. but I agree it seems the most symbolically intuitive
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I take the D operator. No fuss, full ease.
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You know what’s also superior? Leibniz’ biscuits ‘)
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Fractional derivatives seem easier to write in the notation on the right. Though D^{\alpha} (multi-index) notation is quite nice
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Up to a constant ;-)
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