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Let $x,y$ be 2 variables.

When then is ${dx\over dy }= {1\over {dy\over dx}}$? I guess it is true for total derivatives, but am not entirely sure.

What about if the derivatives are only partial derivatives?

Many thanks.

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    Remember that $\dfrac{dy}{dx}$ is defined as some kind of limit of $\dfrac{\Delta y}{\Delta x}$ as $\Delta y$ and $\Delta x$ approach zero. So have a think about why this identity is true, and this may lead you to an answer to your own question.2012-08-21
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    It's true for partial derivatives, if you keep the same variables constant. Remember a partial derivatives needs to specify what you keep constant.2012-08-21
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    I suggest you abandon this medieval language and start thinking in terms of functions and their inverses. Variables are not functions, and derivatives are not fractions.2012-08-21

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