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.
by
Miraj Shah