I was hoping someone could check my solution.

1. Calculate the derivative of:$\displaystyle \frac{\cos x}{\ x-1} $

$\displaystyle f(x)=(cosx)(1-x)^{-1} $

$\displaystyle f'(x)=(cosx)'(1-x)^{-1} + (cosx)((1-x)^{-1})'$

$\displaystyle f'(x)=-sinx(1-x)^{-1} + cosx(-1)(1-x)^{-2}(-1) $

$\displaystyle f'(x)=\frac{\-sinx}{\ 1-x} + \frac {\ cosx}{x^2-2x+1}$

Thanks in advance.

Sincerely,

Raymond MacNeil