Does grad(∂f/∂t) equal ∂/∂t(grad f)?

[M. next]

Is the grad($\frac{\partial f}{\partial t}$) the same as $\frac{\partial}{\partial t}$(gradf)?

Thank you.

 

[tiny-tim]

Hi M. next!

Is the grad($\frac{\partial f}{\partial t}$) the same as $\frac{\partial}{\partial t}$(gradf)?

Unless f is really weird, yes.

(it's the same test as whether ∂²f/∂x∂t = ∂²f/∂t∂x …

i forget the exact conditions)​

 

[M. next]

Thank you!