Time derivative of spherical unit vector

Question

I want to find time derivative of $\hat \phi $ ($(r,\theta, \phi)$ of spherical coordinates). I know that, $$\hat \phi = -\sin \phi \hat i + \cos \phi \hat j .$$ It is only a function of $\phi $. Now, $$\frac {d \hat \phi} {dt}= \frac {d \hat \phi} {d \phi}\cdot \frac {d \phi} {dt} = - \cos \phi \hat i - \sin \phi \hat j .\frac {d\phi} {dt}$$ How to express in terms of $\hat r$ and $\hat \theta$?