I've been trying to solve this for a little while now but I feel kinda lost and I thought you could maybe help me out.
Just in case a picture helps...
is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
In this case...
Just in case another picture doesn't hurt (and in view of comments below)...
Wrapping the chain rule inside the (legs-uncrossed version of) ...
... the product rule, we get...
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!