Ahh they just switched the two chain rule derivatives. Got it. Thank you. Another question: is the second equal sign correct? Why does the first term only have one derivative?
The second equal sign is correct. Apply the product rule. The first term arises from the derivative acting on the vector component and the derivatives outside cancelling (another instance of the chain rule).
But since they are operators, I don't see how the two can cancel each other out and the fact it's the derivative squared so we cannot move one of derivatives to the right and let them somehow cancel out like so:
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