Could someone help me with the following question? The scalar field f and the vector field F in cylindricalcoordinates are given by $\displaystyle f=\frac{cos(\theta)}{r}$ respective $\displaystyle\vec{F} = \frac{cos \theta}{r} \hat{\theta}$
Compute $\nabla f$, $\nabla^{2}f$, $\nabla \cdot F$, $\nabla \times F$
I got $\displaystyle \nabla f=-\frac{cos\theta}{r^2}\hat r-\frac{sin\theta}{r}\hat \theta$
But it is wrong :(( I have exam in two days I should know those calculations :((
EDIT: I think i forgot the scale factors? If yes, then i think i need help with $\nabla \cdot F$, $\nabla \times F$