The derivative $$\dfrac{\mathrm dy}{\mathrm dx}$$ is not a ratio.

Leibniz 引进了符号 $$\dfrac{\mathrm dy}{\mathrm dx}$$, 人们认为它是商: $$x$$ 的改变导致的 $$y$$ 的无穷小改变与 $$x$$ 的无穷小改变的商.

$\frac{\mathrm dx}{\mathrm dy} = \frac1{\frac{\mathrm dy}{\mathrm dx}}.$

$\frac{\mathrm dz}{\mathrm dx} = \frac{\mathrm dz}{\mathrm dy}\frac{\mathrm dy}{\mathrm dx}.$

$\frac{\mathrm dy}{\mathrm dx} = -\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}.$

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