<s>[INST] Maclaurin series expansion Write the Maclaurin series for: $6\cos{5x^2}$ 
Find the first five coefficients. 
For this question: I repeatedly come to the answer of: $6-75 x^4+\frac{625 x^8}{4}+O(x^9)$
With the coefficients being $6, -75, \frac{625}{4}$ and $0$. These answers are wrong though. 
Any suggestions on how to get the 2nd, 3rd, 4th, and fifth coeffient? I have coefficient #1 correct. 
 [/INST] $$
\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \ldots
$$
Thus,
$$
6\cos(5x^2) = 6\biggl[1 - \frac{(5x^2)^2}{2} + \frac{(5x^2)^4}{24} - \frac{(5x^2)^6}{720} + \frac{(5x^2)^8}{40320} - \ldots \biggr]
$$
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