Partial Derivatives: What are They and Why Are They Used?

[sparkle123]

Why can you do this?

thanks!

 

[SammyS]

It can be done if B, as a function of x & t, and its first and second partial derivatives are all continuous.

 

[sparkle123]

Thanks!
How would you know if a function's first and 2nd partial derivatives are continuous?

 

[I like Serena]

Thanks!
How would you know if a function's first and 2nd partial derivatives are continuous?

If you have a formula for B, you can try and evaluate them.

If B is the magnetic field, you can assume so, because our empirical laws of physics say so.
(Most naturally occurring phenomena are infinitely differentiable.)

 

[sparkle123]

Yes, B is the magnetic field! Thanks! :)