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I want to find the gradient vector of f(x,y,z)=2*sqrt(xyz) at the point ((3,-4,-3).

I find the partials and set in for the x-, y-, and z-values, and find the grad. vector (2, (1,5), 2). The right solution is (2, (-1,5), -2), so I have obviously made a mistake with the sqrt. How do I know whether it's + or -?

And another question: Have I used the chain rule correctly when I have calculated the gradient of f(x,y,z) at (-5,1,3) to be (160,-240,400)?

I find the partials and set in for the x-, y-, and z-values, and find the grad. vector (2, (1,5), 2). The right solution is (2, (-1,5), -2), so I have obviously made a mistake with the sqrt. How do I know whether it's + or -?

And another question: Have I used the chain rule correctly when I have calculated the gradient of f(x,y,z) at (-5,1,3) to be (160,-240,400)?

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