I have a function, [itex]x(t)[/itex], where [itex]x[/itex] and [itex]t[/itex] are real scalars. I have been trying to derive an analytical expression for the n(adsbygoogle = window.adsbygoogle || []).push({}); ^{th}derivative of [itex]x[/itex] with respect to [itex]t[/itex]:[tex]x^{(n)}(t) \triangleq \frac{d^n}{dt^n}x(t)= \ \ ?[/tex]However, getting a general expression is proving tricky.

Meanwhile, I have managed to derive a method for recursively obtaining the n^{th}derivative of [itex]t[/itex] with respect to [itex]x[/itex]:[tex]t^{(n)}(x) = f\{t^{(n-1)}(x), t^{(n-2)}(x), \dots\} = \ \ \mathrm{known}[/tex]

Is there any way I can use this information to my advantage?

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# How to derive nth derivative of x(t), when nth derivative of t(x) is known?

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