Calculating the fifth derivative

So I've got this problem:

Calculate the fifth derivative of the function

I tried going through the hassle of doing product rule again and again but it became so messy by the third iteration that I have to believe that there is an easier way to solve this problem (and perhaps other problems like it?).

Thanks.

Re: Calculating the fifth derivative

Hey Paze.

The way you are doing it is the way to do it (and yes it will probably be very messy).

Re: Calculating the fifth derivative

Re: Calculating the fifth derivative

Actually, not all that messy.....

- Hollywood

Re: Calculating the fifth derivative

Quote:

Originally Posted by

**hollywood** Actually, not all that messy.....

- Hollywood

Care to explain? It becomes pretty messy for me.

Re: Calculating the fifth derivative

If you apply the product rule to , you get . So if you start with and apply it 5 times, you get .

- Hollywood

Re: Calculating the fifth derivative

Quote:

Originally Posted by

**hollywood** If you apply the product rule to

, you get

. So if you start with

and apply it 5 times, you get

.

- Hollywood

Where does that n come from? I just did product rule on and somehow, natural logarithms started getting mixed and what not.. :(

Re: Calculating the fifth derivative

n is any integer.

So when you take the first derivative, you get . You can write that . Now try taking the derivative again.

- Hollywood

Re: Calculating the fifth derivative

Re: Calculating the fifth derivative

its easy the nth derivative of xe^x is e^x[x+n] as simple as such.