Hi...if you want a really dumed down explanation of the chain rule, listen to this...
If you hold a chain up in the air and dangle it, the bottom link relies on the link above it, and the link above that relies on the next one up, and so on...
Remember the acronym PEMDAS ? Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction ? Well the P is more powerful than the E, and the E is more powerful than the M and so on...kinda like a Chain...
In your problem, (4x+4)^-3 , the big bully would be the -3, and the bully is standing on top of the poor kid named (4x+4), so if you think of it that way, deal with the exponent first...bring that dirty bully down in front, leave the poor kid in the box alone, then take 1 away from what used to be the exponent...then after the bully was taken care of, let the poor beat up kid outta the box and work his derivative which would be 4...all that gets separated and multiplied together...
One thing to note however, unlike PEMDAS where you absolutely had to do P before E and so on, you could actually do the chain rule in reverse...
You could actually let the poor beat up kid outta the box first, then take care of the bully...this is okay to do because everything is multiplied together in the end and the answser works out to be the same!!! See my picture for clarity...HOPE THIS HELPS!!! GOOD LUCK!