Question

If f(x) = x/(x-1), find a formula for f^(n)(x).

Answer 1

start by finding first few derivatives : f', f", f''', f''''...

Answer 2

\[f \prime=\frac{ -1 }{ (x-1)^2 }\]
\[f^{(2)}=\frac{ 2.1 }{ (x-1)^3 }\]
\[f^{(3)}=-\frac{ 3.2.1 }{ (x-1)^3 }\]
\[f^{(n)}=(-1)^n\frac{ n! }{ (x-1)^{n+1} }\]

Answer 3

What grade is this for? Thanks is pre calculus,right?

Answer 4

This *