# What will you try?

Calculus Level 5

$\large f(x)=\frac{1}{1-x+x^2}$

If $f_6(x) = \frac ab \sin^c \left( \text{arctan} \left( \frac {\sqrt d}{ex-f} \right) \right) \sin \left( g \cdot \text{arctan} \left( \frac {\sqrt d}{ex-f} \right) \right)$

where $$a,b,c,d,e,f,g$$ are integers independent of $$x$$. Evaluate: $$a+b+c+d+e+f+g$$.

Details and Assumptions:

• $$f_n(x)$$ denotes $$n^\text{th}$$ derivative of $$f(x)$$

• The greatest common divisor between $$a$$ and $$b$$ is 1/

• $$d$$ is square free.

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