What is the coefficient of X^12 in the Maclaurin series for (cos(3x^3))/4

Question

This is all the information I got and I really don't understand it

Answer 1

We use Maclaurin series: cosu = 1 - u²/2! + u⁴/4! - ...; cosu/4 = 1 - u²/8 + u⁴/96 - ...

Now let set u = 3x³, then cos(3x³)/4 = 1 - 9x⁶/8 + 81x¹²/96 - ... = 1 - 9x⁶/8 + 27x¹²/32 - ..

So, coefficient of x¹² is equal 27/32