In my classical mechanics course, the professor did a bit of algebraic wizardry in a derivation for one of Kepler's Laws where a second derivative was simplified to a first derivative by taking the square root of both sides of the relation. It basically went something like this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{d^2 u}{dx^2} = \big( f(x)\big)^2\\ \frac{d u}{dx} \frac{d u}{dx} = \big( f(x)\big)^2

\\\frac{d u}{dx} = f(x) [/tex].

Why could my professor do this? How does this make sense in a physical sense? Or in a mathematical sense? What are the cases for where this trick won't work? Any clarification is much appreciated.

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# I "Undo" Second Derivative With Square Root?

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