Can I pull a time derivative outside of a curl?

[L_landau]

Homework Statement

For the equation ∇ x E = -∂B/∂t I took the curl of both sides to get

∇ x (∇ x E) = ∇ x -∂B/∂t

I feel like it'd be very wrong to pull out the time derivative. Am I correct?

 

[ehild]

Homework Statement

For the equation ∇ x E = -∂B/∂t I took the curl of both sides to get

∇ x (∇ x E) = ∇ x -∂B/∂t

I feel like it'd be very wrong to pull out the time derivative. Am I correct?

No, you can pull out the time derivative.

 

[Ray Vickson]

Homework Statement

For the equation ∇ x E = -∂B/∂t I took the curl of both sides to get

∇ x (∇ x E) = ∇ x -∂B/∂t

I feel like it'd be very wrong to pull out the time derivative. Am I correct?

Yes, this is just the property of interchangeability of partial derivatives: $\partial / \partial t \; \partial / \partial \psi f(\psi,t) = \partial /\partial \psi \; \partial / \partial t f(\psi,t)$.