Extended product rule for derivatives

[musicfairy]

Can someone please explain it to me? My handwriting wasn't at its best when I was taking notes in class and now I can't read it. The teacher showed an example that I jotted down but what's the general rule?

 

[Pere Callahan]

Maybe you should consult your textbook or take notes more carefully.
The usual product rule for differentiation reads
$$(uv)'=uv'+u'v$$
where u,v are functions.

What do you mean by extended product rule?

 

[musicfairy]

I meant if you have 3 or more terms, like y = sinxcosxlnx and you want the derivative.

 

[cristo]

For three terms: (uvw)'=(uv)'w+(uv)w'=u'vw+uv'w+uvw'.

As you can see, this can be extended to 4 terms and beyond quite readily.

 

[nicksauce]

It's easy to derive yourself, using the regular problem rule. If you have y = f(x)g(x)h(x), then use the formula Pete Callahan posted, using u=f(x), v=(g)h(x).
So then y' = uv' + vu'
Then use the product rule again to find v'

 

[musicfairy]

Thanks everyone. This makes more sense now.