... is the product rule for differentiation. Straight lines differentiate downwards with respect to x.

... is lazy integration by parts, doing without u and v. But into this we are going to embed...

... the chain rule. Straight continuous lines again differentiate downwards (integrate up) with respect to the main variable (in this case 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).