Simpson's Rule - Finding the fourth derivative - an easier way?

[Asphyxiated]

Homework Statement

This is really just a shot in the dark here but I am hoping that there is something that I have forgotten about derivatives. Is there a way to directly find a:

$$y^{(n)} = f(x)$$

?

That is, is there a way to directly find the nth derivative of y without computing n derivatives?

Since Simpson's Rule needs the 4th derivative of a function it can get very tedious and complicated computing 4 derivatives. Just the 3rd derivative of:

$$y = \frac{1}{1+x^{2}}$$

took a very long time to get to...

 

[Asphyxiated]

I take it that I didn't forget and I am left to do the tedious work... \sigh

 

[LCKurtz]

Homework Statement

This is really just a shot in the dark here but I am hoping that there is something that I have forgotten about derivatives. Is there a way to directly find a:

$$y^{(n)} = f(x)$$

?

That is, is there a way to directly find the nth derivative of y without computing n derivatives?

No. There are functions that have nice closed formulas for the nth derivative, but those come by establishing a pattern and using induction.

Since Simpson's Rule needs the 4th derivative of a function it can get very tedious and complicated computing 4 derivatives. Just the 3rd derivative of:

$$y = \frac{1}{1+x^{2}}$$

took a very long time to get to...

Actually calculating the integral by Simpson's rule doesn't involve any derivatives. It is estimating the error that does. But, yes, if you are doing it by hand, there is no shortcut.

 

[Asphyxiated]

Thats what I meant was for the error estimate, but thanks for the help man, I didn't really think so but i was just hopeful.