How do you find the derivative of #1/(x+1)^2 #?
Method 1: Brute Force
Since this is a simple reciprocal, we can write it as a power and then use the chain rule:
This answer seems so simple, we could have almost done it by inspection.
Method 2: Substitution
One way to prove this to ourselves is to do a substitution by setting
which allows us to do the following substitution
now we end up with the very simple derivative in terms of
which we can substitute back in for
Just as we had before, but we can see why the problem was really very simple after all
Method 3: Inspection
The offset of