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

question 97

Multiple Choice

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

---

Definitions:

Loan Agreement

A formal contract between a borrower and a lender outlining the terms and conditions of the loan, including interest rates and repayment schedule.

Installment Notes

A debt instrument that requires a series of payments over time, often used for financing purchases.

Payment Pattern

The typical manner or schedule in which a business or individual settles their financial obligations, such as monthly or quarterly payments.