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Math Help - Maclaurin Series - find nth derivative

  1. #1
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    Maclaurin Series - find nth derivative

    I have a WebWork problem that gives me :

    f(x)=[cos(2x^2)-1]/(x^3)

    and it asks me to find the 9th derivative at 0. It gives me a hint that I should use the Maclaurin series of f(x).

    So far, I found f(x) in summation form. I first found cos(2x^2), subtracted -1, and then divided each term by x^3. At the end I get the equation attached to this post. I don't know how to proceed...

    I thought that f(9nthDerivative)(0)/9! is equal to the constants of the ninth term in the summation. i'm really stuck. Can someone help me?

    Ps. sorry, I'm new to the forum and I don't know how to add equations :S
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  2. #2
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    Quote Originally Posted by makarooney View Post
    I have a WebWork problem that gives me :

    f(x)=[cos(2x^2)-1]/(x^3)

    and it asks me to find the 9th derivative at 0. It gives me a hint that I should use the Maclaurin series of f(x).

    So far, I found f(x) in summation form. I first found cos(2x^2), subtracted -1, and then divided each term by x^3. At the end I get the equation attached to this post. I don't know how to proceed...

    I thought that f(9nthDerivative)(0)/9! is equal to the constants of the ninth term in the summation. i'm really stuck. Can someone help me?

    Ps. sorry, I'm new to the forum and I don't know how to add equations :S
    Note that the Maclaurin series formula is f(x) = f(0) + f'(0) x + \frac{f''(0)}{2!} x^2 + \frac{f^{(3)}(0)}{3!} x^3 + .... + \frac{f^{(9)}(0)}{9!} x^9 + ....

    so get the coefficient of x^9 in the series you found and do with it what should be the obvious thing ....
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  3. #3
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    Oooh, ok. I thought that I needed to find the ninth term! I got it now, it works! Thank you!
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