Product rule for two derivatives

[fiziksfun]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

I just want a formula without a proof

 

[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.

 

[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.