Laplacian is also about the second derivatives. Why are there two quantities (Laplacian and Hessian) associated with the quadratic terms? How are they related?

blahaj

are 3rd derivatives ever useful?

vtnguyen

Is the Hessian always symmetric because the order of differentiation doesn't matter?

Oh_skr

Does f here need to have continuous second derivatives in order for the order of differentiation to be irrelevant?

dl123

Will higher order derivatives ever be used in practice?

Laplacian is also about the second derivatives. Why are there two quantities (Laplacian and Hessian) associated with the quadratic terms? How are they related?

are 3rd derivatives ever useful?

Is the Hessian always symmetric because the order of differentiation doesn't matter?

Does f here need to have continuous second derivatives in order for the order of differentiation to be irrelevant?

Will higher order derivatives ever be used in practice?