# 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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