\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) = \left( {\frac {\ln  \left( -1+y \left( x \right)  \right) y \left( x \right) }{ \left( 1-y \left( x \right)  \right) \ln  \left( x \right) x}}-{\frac {\ln  \left( -1+y \left( x \right)  \right) }{ \left( 1-y \left( x \right)  \right) \ln  \left( x \right) x}}-f \left( x \right)  \right)  \left( 1-y \left( x \right)  \right) =0}
\]