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For example, could I write something like the following? $$f'(x) = \frac{d}{dx}x^2$$

Since Newton's notation and Leibniz's notation end up meaning the same thing, I wondered if this is generally considered to be good form.

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    Yes of course you can. A precision: notation f'(x) is **not** Newton's. It has been defined many years after the death of Newton, I think by Euler (to be checked) circa 1750. Newton uses dots over the quantities he derives (with respect to time in general). – 2017-01-08
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    @JeanMarie Thanks for the heads up. Is there a need to change the question, by the way? (Happy belated NY's!) – 2017-01-08
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    It is not of fundamental importance now, but historically, there has been a big conflict between Newton and Leibniz (the man of d/dx) co-inventors of differential calculus, not that much about notations but about the underlying concepts. Btw: Happy new year to you too! – 2017-01-08
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    @Max Li : Please the question I had asked http://math.stackexchange.com/questions/1966777/newton-vs-leibniz-notation – 2017-01-08

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