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Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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How to continually simplify derivatives of function defined in a system? [closed]

For example, if I input something like b'[t_] = a[t]; a'[t_] = -Sin[b[t]]; a''[t] it outputs just a''[t]. Is there a way to get Mathematica to always simplify any derivatives of a and b to expressio …
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