Are the second mixed partial derivatives of binary elementary functions continuous? Are they equal? Are they differentiable?

Are the second mixed partial derivatives of binary elementary functions continuous? Are they equal? Are they differentiable?

Differentiable must be continuous, continuous not differentiable
Must be continuous, not necessarily differentiable, not necessarily equal
It's useless for a long time. I can't give specific examples

The continuity of two mixed second order partial derivatives of the function z = f (x, y) in the domain D is a sufficient condition for the equality of the two mixed second order partial derivatives in the domain D. why?

Let z = arctany / x, then the second partial derivative of Z with respect to y is?

z=arctany/x
δz/δy = 1/[1+(y/x)^2] * [1/x] = x/[x^2+y^2]
δ²z/δy² =δ(δz/δy)/δy = -x(2y)/[x^2+y^2]^2 = -2xy/[x^2+y^2]^2

Does the domain of definition change after derivation

The domain of definition of function is different from that of derivative function after derivation
Y = under the cubic root (x - 1)
Here x can be 1;
dy/dx = (1/3)(x - 1)^(-2/3)
The definition field of derivative function dy / DX, X ≠ 1

How to pronounce the sign of partial derivative? How did it come from?
What is it in English?

In 1755, Euler used the sign for partial derivatives and partial derivatives to express the partial derivatives of pairs

∂ is the sign of partial derivative in higher number?

&#The French invented round
Usually we read it as "Pian",
For example, &; Z / &; X, read as biased Z rather than unbiased X

How do you read the sign of the partial derivative?

In 1755, Euler used to express the partial derivative of a pair, which has a very wide application. But when it is with power exponent, it can't be distinguished from the general derivative, such as the square or the square? After that, in 1776, Euler used to express the partial derivative of a pair, In 1770, Condorcet used to express the partial differential of a pair and the partial differential of a pair. In another place, he also used to express the total differential and the partial differential. The most significant work is Lagrange's work. In 1786, he used to read "rounded" to express the partial derivative, He used to denote the partial derivative of a pair. This is the modern symbol of partial derivative. But this symbol did not immediately get general use until Zhike emphasized this symbol again in 1841, and introduced d to denote total differential and partial differential. If it is a function of sum, then this symbol will be widely used after total differential

How to pronounce the standard pronunciation of "@"?

@At (same as at)
Pronunciation of Pinyin: AI te
Transliteration of "Aite"
It's hard to type the phonetic
There are two ways to read it. One is the inverted E and t
The other is fameihua and t

How to pronounce?

Meaning: and
Pronunciation: and

Let z = f (x, y) be a function with continuous partial derivatives determined by the equation E ^ 2z-2xyz = 0
Let z = f (x, y) be a function with continuous partial derivatives determined by the equation E ^ 2z-2xyz = 0?