Question #225909

If Ø(x, y, z) = x² - y²-2²-2, then ∇Ø at (2,1,-1) is

A) 4i +2j-2k

B)4i-2j-2k

C) 4i + 2j + 2k

D)4i - 2j +2k

Expert's answer

"\u00d8(x, y, z) = x\u00b2 - y\u00b2-z\u00b2-2\\\\\nThen \\space \u2207\u00d8= \\frac{\\partial}{\\partial x}i, \\frac{\\partial}{\\partial x}j, \\frac{\\partial}{\\partial x}k\\\\\n\u2207\u00d8= \\frac{\\partial}{\\partial x} (x\u00b2 - y\u00b2-z\u00b2-2), \\frac{\\partial}{\\partial x}(x\u00b2 - y\u00b2-z\u00b2-2), \\frac{\\partial}{\\partial x}(x\u00b2 - y\u00b2-z\u00b2-2)\\\\\n\u2207\u00d8=2x i, 2yj,2zk\\\\\n At (2,1,-1) \\\\\n\u2207\u00d8=4 i+ 2j-2k"

Option A is correct.

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