Be patient, I'll explain it to you slowly:

1 and dy/dx indicate that y is a function of x, and the change of x causes the change of y, and the ratio of the change is the derivative, which is the slope.

2. Most of the functions we usually encounter are explicit functions, that is, we can solve Y and express Y with X. ..

3. But in most cases, our equations can't be solved, that is, we can't write the form of y=f(x), for example, the solution of y+siny = ln(x+y)+3, 100 can't be solved for a lifetime! ! Such a function is called

An implicit function.

4. When encountering an implicit function, remember that Y is a function of X, and our derivation is to derive X, not Y, and Y only plays an intermediate role in the composite function! For example, y 2, we take the derivative of x, because of the compound relationship, we take the derivative of y first, that is, d (y 2)/dy = 2y. Y 2 is a compound function. After taking the derivative of Y, we get 2y, but Y is still a function of X, so we should continue to take the derivative of Y to X, that is, there is also a dy/dx.

Together, it is: d (y 2)/dx = [d (y 2)/dy] * [dy/dx] = 2y * dy/dx.

5. If the compound relationship involves more levels, such as Y is a function of U, U is a function of V, V is a function of W, and W is a function of X. Now, if you want to take the derivative of X, you must chain it step by step:

dy/dx =[dy/du]*[du/dv]*[dv/dw]*[dw/dx].

If you haven't made it clear, please contact me, and I will help you voluntarily online. Okay？