Proving grad(v_ . r_) = v_ with Spherical Polars | Math Gradient Help

[c299792458]

Homework Statement

hi, any help with proving that grad (v_ . r_) = v_ using spherical polars, where v_ is a uniform vector field would be great
it is trivial to prove using summation convention or cartesian coordinates but having to use spherical polars looks messy...

thanks

Homework Equations

as above/below...

The Attempt at a Solution

i know the identity: grad (a_.b_) = a x curl b + b x curl a + a . grad b + b . grad a
is it true that curl v_ and grad v_ are 0 since v_ is a uniform field? and grad r_ is the unit vector of r_? and curl r_ is 0? where i think r_ is the position vector...

 

[fzero]

You will obviously want to know the form of the gradient in spherical coordinates http://en.wikipedia.org/wiki/Spheri..._and_differentiation_in_spherical_coordinates as well as the relations between the unit vectors in spherical and Cartesian coordinates http://en.wikipedia.org/wiki/Unit_vectors#Spherical_coordinates It's not that bad. Give the computation a try and come back if you get stuck.

 

[c299792458]

solved :)
thanks for the links, fzero