Thread: "Let f and g be twice differentiable functions ..." - Derivitive problem

There's a problem that our professor wanted us to look at and I'd really like to understand it. It says

"Let f and g be twice differentiable functions. Derive a formula for (fg'') = [(fg)']' using your knowledge of differentiation rules."

We know about the power rule and chain rule and all that fun stuff .. I guess I'm not sure what she's asking.

Am I trying to apply these rules to "[(fg)']'" to make it look like (fg'')? If I am, I don't know how I would even start that.

Any help would be appreciated.

Thanks

To start with, you may note that



by the Product Rule. By linearity,

Originally Posted by JTG2003

There's a problem that our professor wanted us to look at and I'd really like to understand it. It says

"Let f and g be twice differentiable functions. Derive a formula for (fg'') = [(fg)']' using your knowledge of differentiation rules."

We know about the power rule and chain rule and all that fun stuff .. I guess I'm not sure what she's asking.

Am I trying to apply these rules to "[(fg)']'" to make it look like (fg'')? If I am, I don't know how I would even start that.

Any help would be appreciated.

Thanks

your notation should be






so ...

Hm... ok, I think I get it.

It will take a few times of going through it I guess.

Thank you.