... is the product rule, straight continuous lines differentiating downwards with respect to x.
Then, for the other pic, we have also...
... the chain rule. Straight continuous lines 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).
(Wrapped inside the legs uncrossed version of the product rule.)