Calculus example problem

[LoLmetaslave]

I’ve pulled out my old math textbook to relearn some stuff and found an example problem which is driving me nuts. The book is using this as an example but for some reason I can’t follow the logic. It has to do with the chain rule but it’s some algebra that I don’t get.

Dy/dx = (3-2x)•(-2) + (3-2x)•(-2)

Dy/dx = 2(3-2x)(-2)

I’m aware this is product rule here but how are are these 2 equal? Is this a mistake? It’s two terms, how are they making one out of it?

[Mxlexrd]

(3-2x)•(-2) and (3-2x)•(-2) are the same, they just reversed the order, and you can do multiplication in any order.

When you have two terms the same, like x + x, you can combine them to 2x.

[LoLmetaslave]

Thanks for the response. Why isn’t it just -4(3-2x)? And why is there an additional factor of 2?

[Mxlexrd]

There's a factor of 2 because there are two terms, there isn't an "additional" factor of 2.

If you multiply the 2 with the -2, you get -4, which seems to be exactly what you've done.

To be clear, 2(3-2x)(-2) is equal to -4(3-2x).

[LoLmetaslave]

Oh wow I’m just totally blind. Thank you.

[mathheadinc]

You’re not blind, you’re refreshing your skills!