If y = f (x) is a differentiable function, then when △ x → 0, △ y-dy is the infinitesimal of △ X（

Infinitesimal of the same order or infinitesimal of higher order
Because of the existence of the first derivative, this derivative may be zero,
When Lim △ X / △ y = 0, △ x is a higher order infinitesimal of △ y
When Lim △ X / △ y is not equal to 0, △ x is an infinitesimal of the same order of △ y

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1. It is said that "if y = f (x) is differentiable at point x, then when △ x → 0, the differential dy of the function at point x is infinitesimal of the same order of △ X." Is this statement correct? Why? The answer is incorrect. Please explain
2. Let f (x) be differentiable, then when △ x → 0, △ y-dy is infinitesimal of higher order compared with X,
3. If f (x) is a differentiable function, then dy is a linear function of △ X Why? Dy = f '(x) △ x, f (x) is a function of X, also called the linear function of △ x?
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5. Is the partial derivative of a function independent of the order of derivation
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18. For example, for the function y = X-1, let y = 0, we can get x = 1, we say 1 is the zero point of the function y = X-1 The known function y = x 2 - 2mx - 2 (M + 3) (M is a constant) (1) When m = 0, find the zero point of the function; (2) It is proved that no matter what value m takes, the function always has two zeros; (3) Let the two zeros of the function be x 1 and x 2 respectively. At this time, the intersection of the function image and the X axis is a and B respectively (point a is on the left side of point B), and point m is on the line y = X-10. When Ma + MB is the minimum, the analytic expression of the function of the line am is obtained
19. For example, for the function y = X-1, let y = 0, we can get x = 1, we say 1 is the function y = X-1
20. For example, for the function y = X-1, let y = 0, we can get x = 1, we say that 1 is the zero of the function y = X-1. It is known that the function y = x2-2mx-2 (M + 3) (M is a constant). (1) when m = 0, find the zero of the function; (2) prove that no matter what value m takes, the function always has two zeros; (3) let the two zeros of the function be respectively The intersection of function image and X axis is a and B respectively (point a is on the left side of point B), and point m is on the line y = X-10. When Ma + MB is the minimum, the function analytic expression of line am is obtained