Finding Derivative of a Complex Expression: Tips and Tricks

[Checkfate]

Arg I am banging my head trying to figure this one out.

The question is :

Differentiate y=$$x^{6}(x-1)^{10}(x+2)^{8}$$

I have dealt with mannnny questions with two terms multiplied together and then I just use a combination of the chain rule and the product rule etc. This one is different though. I have tried the chain rule (multiplying each term by the derivative of each term) to no avail. I got an answer with about 50 terms in it and when I checked on my calculator for what the derivative should be... it's not correct. It doesn't even equal out. Anyways, I don't want an answer :P Can someone just point me in the right direction? Thanks!

 

[arildno]

Set $$y(x)=f(x)*g(x)*h(x)$$
Figure out what f, g and h ought to be.
Then, you have:
$$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$$

 

[Checkfate]

Hmm

Was just looking around on the net and the rule you mentioned is called the triple product rule, but they don't show it in my textbook... No idea how they wanted me to figure it out. lol. Thanks a lot :)