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**1. Homework Statement**

Determine the Taylor series for the function below at x = 0 by computing P

_{5}(x)

f(x) = cos(3x

^{2})

**2. Homework Equations**

Maclaurin Series for degree 5

f(0) + f

^{1}(0)x + f

^{2}(0)x

^{2}/2! + f

^{3}(0)x

^{3}/3! + f

^{4}(0)x

^{4}/4! + f

^{5}(0)x

^{5}/5!

**3. The Attempt at a Solution**

I know how to do this but attempting to solve the 3rd derivative of cos(3x

^{2}) and onward is simply infeasible due to it requiring multiplication rule and stuff

I remember my professor mentioning some sort of short cut to certain series

Is there a short cut or heuristic to solve this or do I simply have to solve the higher order derivatives?

Update

I tried solving the series as cos(u) where u = 3x

^{2}and got

1 - 9x

^{4}/2 + 27x

^{8}/8

which matches the result from a Taylor Series calculator online

I feel like I am making a basic mistake right now please enlighten me

Update

Genius me did not realize that I needed to stop at the 4th degree even after doing to replacement

1 - 9x

^{4}/2

was accepted as the correct answer

I guess I ended up answering my own question

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