How is the series relevant?

Calculus Level 3

If we know that the Maclaurin series of \( \sin(x^2) \) is

\[ x^2 - \dfrac{x^6}{3!} + \dfrac{x^{10}}{5!} - \dfrac{x^{14}}{7!} + \cdots , \]

then what is the value of the \(10^\text{th}\) derivative of \( \sin(x^2 ) \) at \(x=0\)?

\[\] Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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