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I searched through a bunch of sites and articles but I could not find the answer to my question anywhere. Hopefully not because of my complete search incompetence.

Is it okay to write a function in the "denominator" of Leibniz notation like this:

$$\frac{d}{d(x+2)}[(x+2)^5]$$

To mean differentiation with respect to x+2, treating x+2 as the variable. This seems extremely useful to me, especially when writing things like the chain rule; This notation makes it clear and understandable in my opinion.

Thank you for your time.

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As long as it is clear I think that most mathematicians would accept it, although some might frown upon it.

One problem is when the expression that is differentiated can be given by the "denominator" in more than one way. For example, if you write $\frac{d}{d\sin x}\cos x,$ should it be interpreted as $\frac{d}{d\sin x}\sqrt{1-\sin^2 x}$ or as $\frac{d}{d\sin x}\left(-\sqrt{1-\sin^2 x}\right)$? It needs to be specified here whether $\cos x>0$ or $\cos x<0.$

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