Let f (x) be differentiable, then when △ x → 0, △ y-dy is infinitesimal of higher order compared with X,

It can be seen from the definition of differential of function

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1. 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?
2. The relation between continuity and differentiability of binary function For example, if f (x, y) is continuous at point (0,0), then if x and y are all close to 0, f (XY) / (| x | y |) exists, is f (XY) differentiable at point (0,0) I know how to smoke The denominator is (| x | plus | y |)
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11. 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
12. If y = f (x) is a differentiable function, then when △ x → 0, △ y-dy is the infinitesimal of △ X（
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