Z = Z (x, y (Z, x)), for both sides of X partial derivative, &; Z / &; X can be eliminated The original problem, z = Z (x, y (Z, x)), and &; Z / &; y is not equal to 0, find &; Y / &; X The answer is as follows: take partial derivatives of X on both sides of the equation, and you will get 0 = &; Z / &; X + &; Z / &; y * &; Y / &; X I don't understand here

Z = Z (x, y (Z, x)), for both sides of X partial derivative, &; Z / &; X can be eliminated The original problem, z = Z (x, y (Z, x)), and &; Z / &; y is not equal to 0, find &; Y / &; X The answer is as follows: take partial derivatives of X on both sides of the equation, and you will get 0 = &; Z / &; X + &; Z / &; y * &; Y / &; X I don't understand here

The Z to the left of the equal sign corresponds to a constant independent of X, so the result of the derivation of X is 0
There are brackets after Z on the right side of the equal sign, indicating that this is a function of two parameters x, y (Z, x). Moreover, both parameters are related to X
The second parameter is y and Y is a function of Z (in this case, Z is equivalent to a constant independent of x) and X, so the partial derivative of the second parameter with respect to X is: &; Z / &; y * &; Y / &; X
The key to this problem is to find out when Z is a function of X and a constant independent of X
On the left side of the equal sign: there are no brackets after Z, so it is equivalent to a constant. On the right side of the equal sign, there are brackets after Z, so it is a function