# nth derivative

• May 12th 2010, 08:24 AM
alexgo
nth derivative
I can't figure this out.
i need the nth derivative.
y=(x^2+x-1)/(x-1)
f'x = (x^2-2*x)/(x-1)^2
f''x = 2/(x-1)^3
f'''x = -6/(x-1)^4
f''''x = 24/(x-1)^5
• May 12th 2010, 08:32 AM
Failure
Quote:

Originally Posted by alexgo
I can't figure this out.
i need the nth derivative.
y=(x^2+x-1)/(x-1)
f'x = (x^2-2*x)/(x-1)^2
f''x = 2/(x-1)^3
f'''x = -6/(x-1)^4
f''''x = 24/(x-1)^5

Note that $f(x)=\frac{x^2+x-1}{x-1}=x+2+\frac{1}{x-1}$.
Thus, appart from the 0th and the 1st derivative, you have $f^{(n)}(x)=\frac{d^n}{dx^n}\frac{1}{x-1}=\frac{(-1)^n n!}{(x-1)^{n+1}}$