Help with calculating the Curl of [f(r)r_vec] I need to show that the $\partial_x [f(r)(\vec{r})]=0$

Is the way to start this by saying that $\vec{r} = (x,y,z)?$

Then $r = \sqrt{x^2+y^2+z^2}?$

I am not sure if this is the way to start because we dont know what the function is?
It is not clear what you are trying to calculate: the title suggests $ \nabla \times ( f(r) \vec{r}) $ but you write $ \partial_x ( f(r) \vec{r} ) $. Since it is not generally true that $ \partial_x ( f(r) \vec{r} ) = 0 $, I'm assuming you are trying to show $\nabla \times ( f(r) \vec{r}) $. Do you know that $ \nabla \times ( \nabla g) = 0 $ for any $ g $? And as a special case, you can try $ g(r) = \int_0^r f(r') r' dr' $. Otherwise you can do it brute force by looking at (http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates) for the formula for $ \nabla \times $ in spherical coordinates.
It is not clear what you are trying to calculate: the title suggests $ \nabla \times ( f(r) \vec{r}) $ but you write $ \partial_x ( f(r) \vec{r} ) $. Since it is not generally true that $ \partial_x ( f(r) \vec{r} ) = 0 $, I'm assuming you are trying to show $\nabla \times ( f(r) \vec{r}) $. Do you know that $ \nabla \times ( \nabla g) = 0 $ for any $ g $? And as a special case, you can try $ g(r) = \int_0^r f(r') r' dr' $. Otherwise you can do it brute force by looking at (http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates) for the formula for $ \nabla \times $ in spherical coordinates.