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Also, as an extension to this question, if it is the case that the free variable ##x## is just there for convenience, then how would we right the differentiation operator ##\frac{\mathrm{d} }{\mathrm{d} x}##? Would you write it as ##\frac{\mathrm{d} }{\mathrm{d} (~)}## or something? Also, would one even be able to define the derivative ##\displaystyle\lim_{\Delta x\rightarrow 0}\frac{f(x + \Delta x ) - f(x)}{\Delta x}## without the use of the free variable ##x##?