Why doesn't the rotation of a curl equal the curl of a rotation, if both curl and the rotation are linear.

Question

I was trying to get the curl of some rotated vector field $\nabla \times R_{ij}n_j(\vec{r})$.

I tried taking ou the rotation matrix $R$.

$$R_{ij} \nabla \times n_j(\vec{r})$$

If $n=(0,f(x),0)$ the curl is $(0,0,f'(x))$.

If I rotate it $n' = (f(x)/ \sqrt{2},0,f(x)/ \sqrt{2})$ the curl is $(0,f(x)/ \sqrt{2},0)$ which is not the corresponding rotation of the original curl.