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1. Homework Statement

1. Homework Statement

"For every differentiable function f = f(x,y,z) and differentiable 3-dimensional vector field

**F**=

**F**(x,y,z), the vector field Curl(f

**F**) equals: "

## Homework Equations

curl

**F**= ∇X

**F**

## The Attempt at a Solution

The solution is apparently: fCurl(

**F**)+∇f x

**F**

I am a little lost the process for this question. I attempted to "solve" the problem using a general case. Essentially I let

**F**= <P, Q, R> and multiplied in "f," so f

**F**= <fP, fQ, fR>.

I then took the curl using the formula. I was left with the following:

curl(f

**F**) = <d/dy(fR)-d/dz(fQ), d/dz(fP)-d/dx(fR), d/dx(fQ)-d/dy(fP)>

I am unsure of where to go from here. I originally was going to factor out "f," but then realized that that is not necessarily possible due to it being within the derivative operator. Any suggestions for a next step would be very helpful!