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My professor told us that the following partial derivatives $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ can be represented as $D_z$ and $D_z'$ respectively where $z$ is a function of $x$ and $y$ . Similarly $\frac{\partial^2 z}{\partial x\partial y}= D_zD_z'$

But I have been wondering what would be $\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}$ in this particular shorthand Notation.

I tried searching in Wikipedia and some online sites but I couldn't get the answer.

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    $\begingroup$ This notation is odd because neither $D_z$, nor $D'_z\,,$ tells us with respect to which variable we differentiate. $\endgroup$
    – Kurt G.
    Oct 26, 2023 at 10:32

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