What is the first derivative of \[f(x) = \sum\limits_{n = 1}^\infty \frac{\sin(\pi\times n^2\times x)}{\pi\times n^2}?\]

\(\text{A) } e^{\sin(\frac{\pi^2}{6}x)}\)

\(\text{B) } e^{\tan{x^2}}\)

\(\text{C) } \ln[\sin(\frac{\pi^2}{6})\cos(e^{\sec^{-1}(x^2)}]\)

\(\text{D) } \cos^{-1}(x^x \times \pi^2)\)

\(\text{E) } \sum\limits_{n = 1}^\infty \frac{\sin(\pi\times n^2\times x)}{\pi\times n^2}\)

\(\text{F) None of the above}\)

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