# 2nd derivatives

1. Feb 20, 2009

### TayTayDatDude

1. The problem statement, all variables and given/known data
Determine the second derivative for the following function:

y= (x^2-4)/(x+1)

2. Relevant equations

3. The attempt at a solution

Well, the first derivative is (x^2+2x+4)/(x^2+2x+1)

For calculating the second derivative I can only get as far as (-6x-6)/(x^4+4x^3+6x^2+4x+1)

On an online derivative calculator, the answer is : -(6/(x^3+3x^2+3x+1)) , yet I can't get to it :(

2. Feb 20, 2009

### Tom Mattson

Staff Emeritus
It would be helpful for you to factor the denominator, and then try to take the second derivative.

Your answer is correct. However you need to reduce the fraction to get the result from the online calculator. This would be easiest if you follow my suggestion above: factor the denominator in f'.

3. Feb 20, 2009

### Staff: Mentor

So $$dy/dx = \frac{x^2 + 2x + 1 + 3}{(x + 1)^2} = \frac{(x + 1)^2 + 3}{(x + 1)^2}$$
$$= 1 + \frac{3}{(x + 1)^2} = 1 + 3(x + 1)^{-2}$$

The extra work it took to get the derivative into this form is more than made up by the time saved in getting the next derivative, which can be done by a fairly simple application of the chain rule.

4. Feb 20, 2009

### TayTayDatDude

I have not yet learned the chain rule, and I do not know how to find the derivative of (x+1)^2, other than by expanding it.

so, (-6x-6)/(x+1)^4

Last edited: Feb 20, 2009
5. Feb 20, 2009

### TayTayDatDude

Edit, solved, thanks.