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Differentiation is the set of techniques and results from Differential Calculus, concerning the calculation of derivatives of functions or distributions.
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Taylor Series of a function not showing the right derivatives
The function is the following
$$ f[t, y + \epsilon \eta , \dot y + \epsilon \dot \eta)$$
How is a Taylor Expansion done in a way that is in powers of $\epsilon$?
$$ f[t, y + \epsilon \eta , \dot y + …