Derivative Problem: Deriving the n-th Derivative of f(x)

[temaire]

Homework Statement

Let $$f(x)=\frac{1}{5x-1}, x\neq 1/5.$$ Derive a formula for the n-th derivative $$f^{n}(x).$$


2The attempt at a solution
I have part of the answer right, but I can't figure out the rest. So far, this is what I have:
$$f^{n}(x)=\frac{-5^{n}}{(5x-1)^{n-1}}$$

I'm pretty sure I have the denominator right. I just need help finishing up the numerator.

 

[Mark44]

Try writing your function as f(x) = (5x - 1)^(-1). That will make differentiating easier.