Question
Asked Feb 7, 2020
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find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

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Expert Answer

Step 1

Given function is

Calculus homework question answer, step 1, image 1

 Firstly, we find all first order partial derivatives of f

Calculus homework question answer, step 1, image 2

Step 2

Now, we find the value of these partial derivatives of f at point (-1,2,-2)

Calculus homework question answer, step 2, image 1

Step 3

We know that gradient of f is defined as

Calculus homework question answer, step 3, image 1

Now, at (-1,2,-2), gradient of f is

Calculus homework question answer, step 3, image 2

...

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