Whole question please!
Total derivative of u with respect to x is the bottom row here...
... bearing some resemblance to your version. As always,
... is the chain rule, and...
... the product 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 (which is the inner function of the composite and hence subject to the chain rule).
Don't integrate - balloontegrate!
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