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**Ulysses** Thank to all of you. Now I'm trying to solve the same exercise, but with the function $\displaystyle f(x)=(1+4x^2)^{-1}$ I've tried to make some algebraic work to get the expression I'm looking for, $\displaystyle (1-x)^{-1}$ but I didn't get it.

I've made the first derivative, and a few more, but I think its just necessary the first, as before. I get:

$\displaystyle f'(x)=\diplaystyle\frac{-8x}{(1+4x^2)^2}$

I thought of making $\displaystyle f(x)=\diplaystyle\frac{1}{(1+4x^2)}= \diplaystyle\frac{1-4x^2}{(1+4x^2)(1-4x^2)}=\diplaystyle\frac{1-4x^2}{(1-16x^2)}$

So, when I take the derivative in this last form I get:

$\displaystyle f'(x)=\diplaystyle\frac{-256x^3}{(1-16x^4)^2}$

I'm not sure how to proceed.