Calculus Question

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Question description
Calculus 3, Textbook: Thomas Calculus Early Transcendentals 13th c2014 solutions ISM, Section: 14.6, Problem: 16
I looked up this problem at Chegg.com. Attached are screenshots from that website. I didn’t understand step 2’s gradient of f at P0 = i + 2j + k. Shouldn’t it be (1/2)i + 2j + (1/2)k? If not, why?
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