question_answer

If \[f(x)=(\cos x+i\,\,\sin \,x)\,\,(\cos 2x+i\,\,\sin 2\,x)\]\[(\cos 3x+i\,\,\sin 3\,x)..........(cos\,\,nx+i\,\,sin\,nx)\]and f(1) = 1, then f "(1) is equal to _______.

A)  \[-{{\left[ \frac{n\,\,(n+1)}{2} \right]}^{2}}\]    

B)  \[{{\left[ \frac{n\,\,(n+1)}{2} \right]}^{2}}\]

C)  \[\frac{n\,\,(n+1)}{2}\]             

D)  \[{{\left[ \frac{n\,\,(n+1)\,\,(2n+1)}{6} \right]}^{2}}\]

E)  None of these