If $f ( x ) = \frac { x } { x - 1 } , \text { find a formula for } f ^ { ( n ) } ( x )$

If $f ( x ) = \frac { x } { x - 1 } , \text { find a formula for } f ^ { ( n ) } ( x )$

A) $f ^ { ( n ) } = ( - 1 ) ^ { n } n ! ( x - 1 ) ^ { - ( n + 1 ) }$

B) $f ^ { ( n ) } = n ! ( x - 1 ) ^ { - ( n + 1 ) }$
C) $f ^ { ( n ) } = ( - 1 ) ^ { n } n ! ( x - 1 ) ^ { - n }$
D) $f ^ { ( n ) } = ( - 1 ) ^ { n } n ! ( x - 1 ) ^ { - ( n - 1 ) }$
E) $f ^ { ( n ) } = ( - 1 ) ^ { n + 1 } n ! ( x - 1 ) ^ { - ( n + 1 ) }$
F)
$f ^ { ( n ) } = ( - 1 ) ^ { n } n ! ( x - 1 ) ^ { n + 1 }$

G) $f ^ { ( n ) } = n ! ( x - 1 ) ^ { - n + 1 }$

H) $f ^ { ( n ) } = ( - 1 ) ^ { n } n ! ( x + 1 ) ^ { - ( n + 1 ) }$

Correct Answer:

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