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This derivative has explicity operated on functions of $x$, which makes it still in some sense "with respect to x". One could imagine multiple operations on multidimensional functions...  Powerful ideas, think about \begin{equation}  \int_0^\infty \frac{sin(x)}{x} \;dx = \frac{\pi}{2}  \end{equation}  We could potentially have a situation where we know that \begin{equation}  \int_0^\infty cos(x) \;dx - \int_0^\infty \frac{sin(x)}{x^2} \;dx = -\frac{\pi}{2}  \end{equation}  Contradictory examples to this are  \begin{equation}