# Power Series of f'(x)

1. Apr 24, 2013

### Magnawolf

1. The problem statement, all variables and given/known data

Find the power series of f'(x), given f(x) = x2cos2(x)

2. Relevant equations

Correct me if I'm wrong

3. The attempt at a solution

Can I just take the derivative of the solution I got previously? If so, what's a good way to write the sequence out so I can easily make a series representation. Or is there a better approach to the problem?

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Last edited by a moderator: Apr 25, 2013
2. Apr 24, 2013

### LCKurtz

Looks good. I would multiply the $x^2/2$ into the parentheses and include it under the summation. Then differentiate it.

3. Apr 24, 2013

### Magnawolf

My main problem is trying to figure out how to represent what I'm getting as a series. When I multiply in the x^2 and differentiate I get

x + x - 8x^3 + 4x^5 - (32/45)x^7...

I can't figure it out

4. Apr 25, 2013

### LCKurtz

When you multiply the $\frac{x^2} 2$ in you have$$\frac {x^2} 2 +\sum_{n=0}^\infty\frac{(-1)^n2^{2n}x^{2n+2}}{(2n)!}$$Just differentiate the first term as you did and differentiate under the sum and you will have your formula.

5. Apr 25, 2013

### Magnawolf

When you say differentiate under the sum, do you mean differentiate each term in the sequence or do you mean you can actually take the derivative of the series equation? I tried googling and checking my textbook and I don't know how to take a derivative of a series in equation form, with the n's and such. If you can show me, that'd be great!

6. Apr 25, 2013

### HallsofIvy

Staff Emeritus
Yes, "differentiate under the sum" means "differentiate term by term". I don't know what you mean by "take the derivative of the equation"!

7. Apr 25, 2013

### LCKurtz

If you look at each term inside the sum, it just a constant times a power of $x$. Use the power rule.

8. Apr 25, 2013

### Magnawolf

Oh okay, I got it now. Thanks for everything man!