- #1

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Note that there's a typo in the solution: [itex]\frac{dx^2}{dt^2}[/itex] should be [itex]\frac{d^2x}{dt^2}[/itex].

The top part I understand completely, it's the bottom half I'm confused about. It seems to me that:

[itex]\frac{d^2x}{dt^2} = \frac{d}{dt}(\frac{dx}{dt}) = \frac{dx}{ds}(\frac{\alpha}{2}\sqrt{\frac{K}{m}}e^{-\frac{\alpha t}{2}})[/itex]

In other words, I don't understand where the second group of terms (after the + sign) comes from in the last line. Why is it there?