# Product rule for two derivatives

1. Mar 4, 2009

### fiziksfun

1. The problem statement, all variables and given/known data

I was just wondering if there is a formula for the product rule when you take two derivatives ... ?

2. Relevant equations

I know the product rule for one derivative .. is u'v + uv' !!!

3. The attempt at a solution

I just want a formula without a proof
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 4, 2009

### Dauden

If I'm understanding what you're asking, you want the derivative of the resultant of the product rule. The way to do it is just to treat them as you did with the first derivative.

You know that uv = u'v +uv'

Well that is basically the same as taking the derivative of ab + cd so you have to apply the product rule again to each term.

3. Mar 4, 2009

### Quantumpencil

You mean to find the second derivative after you've used the product rule to find the first derivative?

Just differentiate each term using Product/chain rules as necessary.