I have the following example:
Example that contains my problem
I cannot seem to find out how they go from $ x_{p}\frac{dx_{p}}{dt}$ to $\frac{d}{dt}(\frac{1}{2}x_{p}^{2})$.
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Do you know how to compute (or "expand") the derivative $\frac{d}{dt}(x_p^2/2)$ (using the chain rule)? Recall the rule: $\frac{df(x)}{dt} = \frac{df(x)}{dx}\frac{dx}{dt}$. – Winther Feb 24 '22 at 17:17
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If you integrate and then take the derivative with respect to the same variable, you get your original expression back. – johnnyb Feb 24 '22 at 17:22