def ts_dlldy(y, df):
 return ((((- (df + 1)) / df) / (1 + ((y ** 2) / df))) * y)

def ts_dlldy ( y , df ) : return ( ( ( ( - ( df + 1 ) ) / df ) / ( 1 + ( ( y ** 2 ) / df ) ) ) * y )
derivative of log pdf of standardized (?) t with respect to y notes parameterized for garch .