Differential calculus includes limit, derivative, differential and integral.

Differential is the limit of variation and derivative is the limit of incremental ratio, both of which are limits. Their calculations seem the same, but their concepts are different. One is the total increment and the other is the increment ratio.

Integral is the inverse operation of derivative, and definite integral is the limit of sum.

The whole differential calculus is about limit, because whether you are derivative, differential or integral, their essence is limit. (1) derivative: connecting two points on the function image, this straight line has a slope. When these two points are infinitely close, the slope of the straight line is the derivative. At this point, the straight line is tangent.

(2) Differentiation is to divide the function image (curve) into countless small right triangles.

Among them, the transverse right angle side is dx, the vertical angle side is dy, and the tangent of the lower left right angle is f'(x).

Obviously, in this infinitesimal right triangle, dy=f'(x)dx.

This is the definition of differential.

(3) Integration is the inverse operation of differentiation, just as subtraction is to addition and division is to multiplication.

Derivative and differential:

Differential is a small change, such as dx.

The derivative is WeChat service, and WeChat service is a differential quotient. For example, the derivative of y to x can be written as dy/dx, which is the quotient of the differential of y and the differential of x. Geometrically, the derivative is the slope.

So when you take the differential of y, it should be dy=y'*dx, and there must be dx in your factor, otherwise it is wrong.

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