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## Homework Statement

**r**=x

**i**+y

**j**+z

**k**and r =[itex]\sqrt{x^2 + y^2 + z^2}[/itex] Let f(r) be a C2 scalar function

Prove that [itex]\nabla[/itex]f = [itex]\frac{1}{2}[/itex][itex]\frac{df}{dr}[/itex]

**r**

## Homework Equations

Vector identities?

## The Attempt at a Solution

[itex]\nabla[/itex]f = ([itex]\frac{df}{dx}[/itex] , [itex]\frac{df}{dy}[/itex] , [itex]\frac{df}{dz}[/itex])

= df/d

**r**]?

= [itex]\frac{df}{dr}[/itex][itex]\hat{r}[/itex] (unit vector of

**r**)

= [itex]\frac{df}{dr}[/itex]

**r**[itex]\frac{1}{r}[/itex]?

I'm pretty sure what I've attempted isn't mathematically correct in the slightest, though in my head it seems to make some geometric sense. Am I even close though?

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