The discussion centers on the mathematical proof of the equation ∇f(r) = f'(r)R/r, where r is defined as the vector field and R = xi + yj + zk. Participants express confusion regarding the interpretation of f(r) and its dependency on the vector field R. It is clarified that f(r) is equivalent to f(√(x²+y²+z²)), emphasizing the relationship between the scalar function f and the radial distance r derived from the Cartesian coordinates.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are dealing with vector calculus and need to understand the relationship between scalar functions and vector fields.
Dumbledore211 said: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 said: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?