How is the series relevant?

Calculus Level 3

If we know that the Maclaurin series of sin(x2) \sin(x^2) is

x2x63!+x105!x147!+, x^2 - \dfrac{x^6}{3!} + \dfrac{x^{10}}{5!} - \dfrac{x^{14}}{7!} + \cdots ,

then what is the value of the 10th10^\text{th} derivative of sin(x2) \sin(x^2 ) at x=0x=0?

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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