Finding the nth Derivative of a Rational Function

[powp]

Hello

I have this problem that I cannot get part of. I need function f^(n)(x) for 1/(5x-1). I have been working it out and I know the denominator is going to be (5x-1) ^ (n+1) but can not figure out the top.

So my question is how do I create a statement that evalutes the following

when x = 1 it equal -5
when x = 2 it equals -5 * -10 == 50
when x = 3 it equals -5 * -10 * -15 == -750

any hints would be great

Thanks

Peter

 

[benorin]

Here's a hint

Hello
I have this problem that I cannot get part of. I need function f^(n)(x) for 1/(5x-1). I have been working it out and I know the denominator is going to be (5x-1) ^ (n+1) but can not figure out the top.

Hint: as you differentiate, leave the coefficients factored. The answer your looking for involves a factorial and something else.

 

[powp]

Thanks. This is driving me crazy. I have been thinking is has to do with factorials all this time but not sure in what way.

 

[powp]

Please help

Can anybody please help me I am stuck. Please please please

 

[powp]

Think I finally got it my answer -1^2(n!)5^n*(5x-1)^(-1-n)

Thanks for your help