By the way,
... is the chain rule, here wrapped inside the legs-uncrossed version of ...
... the product rule... the whole thing hopefully no more fearsome than your common or garden quotient 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 subject to the chain rule).
Don't integrate - balloontegrate!
Balloon Calculus: Gallery
Balloon Calculus Drawing with LaTeX and Asymptote!