How do I do this the way I am supposed to? (without differentiating 9 times)
Any help would be greatly appreciated!
Thanks in advance!
Ok I see how to get the summation of arctan(x^3 /4) but then I don't know what to do. Do I just write down the polynomials up to the x^9 power and do something there? What about f^(n) (a) x^n /n! formula ? What I was trying to do before my current attempt was to just do the summation of f^(n) (a) x^n /n! and to replace f^(n) with it's appropriate algebraic expression but it was tough to compute the second derivative and on.
Sorry for being stupid
So you're OK with this, correct?
Now, consider what happens when you take 9 derivatives of this expression.
The first term will eventually become zero (beyond 3 derivatives).
The second term will become a constant. What constant does it become?
The remaining terms will turn into the form where is a constant and is a positive integer. When you substitute into a term of this form, does it make sense that these terms will all become zero?
Therefore, there is only one nonzero term, which is the second term.