When do you use chain rule?
People ask this question all the time. When do I have to use chain rule, and when can I get away with not worrying about it? Usually, they're trying to look for a set of rules they can follow that will tell them when they can ignore chain rule altogether, because it's a hard thing that they want to avoid if they can.
The problem is that, while there are rare instances where applying chain rule won't effect the derivative or the integral, it's much easier to consider chain rule every single time you take the derivative or the integral, rather than trying to figure out when you can ignore it.
The bottom line is that chain rule has to be applied to every single derivative, and every single integral. Sometimes it won't effect the result, but that's only because applying it means you're multiplying by positive one or dividing by positive one. But you're still applying chain rule.