A simple problem pertaining to divergence

[Dumbledore211]

Homework Statement

The problem states that it is required to prove that ∇f(r)=f'(r)R/r where r is the vector field

Homework Equations

∇=(∂/∂x)i + (∂/∂y)j + (∂/∂z)k
R= xi + yj +zk
r = √(x^2+y^2+z^2)

The Attempt at a Solution

The trouble that I am having with this problem is the inability to truly comprehend what f(r) truly means⋅ Is f(r) dependent on the vector field R?

 

[Dumbledore211]

Homework Statement

The problem states that it is required to prove that ∇f(r)=f'(r)R/r where r is the vector field

Homework Equations

∇=(∂/∂x)i + (∂/∂y)j + (∂/∂z)k
R= xi + yj +zk
r = √(x^2+y^2+z^2)

The Attempt at a Solution

The trouble that I am having with this problem is the inability to truly comprehend what f(r) truly means⋅ Is f(r) dependent on the vector field R?

 

[Dumbledore211]

Is f(r) = f(x)i + f(y)j +f(z)k what being meant in the above stated problem?

 

[Ray Vickson]

Homework Statement

The problem states that it is required to prove that ∇f(r)=f'(r)R/r where r is the vector field

Homework Equations

∇=(∂/∂x)i + (∂/∂y)j + (∂/∂z)k
R= xi + yj +zk
r = √(x^2+y^2+z^2)

The Attempt at a Solution

The trouble that I am having with this problem is the inability to truly comprehend what f(r) truly means⋅ Is f(r) dependent on the vector field R?

$f(r) = f\left(\sqrt{x^2+y^2+z^2}\right)$, because $r$ means $\sqrt{x^2+y^2+z^2}$, as you, yourself, have written.