What is the difference between d2x and dx2

Differences:

1. Different degrees of differentiation

d2x and dx? are both differentiated once, while d?x is differentiated twice

< p>2. The differential variables are different

The differential variable of d2x is 2x, the differential variable of dx? is x?, and the differential variable of d?x is x

Understanding:

1. dx can be understood as "when x changes a small value."

2. dy/dx is "when x changes a small value, the ratio of the value of y change to the value of x change".

3. d2x is understood as "when 2x changes a small value", so d2x/dx = 2, because when x becomes larger by 1, 2x has become larger by 2.

4. d^2(x) is actually d(dx), which is "when the rate of change of x changes a little bit", which is the second-order differential.

5. d(x^2) and d(2x) are very similar in form, that is, "when x^2 changes by a small amount".

Extended information:

In 1675, Leibniz introduced "dx" and "dy" to represent the differentials of x and y respectively. They were first seen in 1684. This symbol has been used in published books to this day. The differential symbol d takes the first letter of differential in English (difference means gap, difference). The English words related to the concept of differential and the symbol d are divide, decrease, and delta. etc. In addition, the symbol D is also called the differential operator.

There is a humorous joke about differentials.

The constant function and the exponential function e^x were walking on the street and saw the differential operator from a distance. The constant function was frightened and hurriedly hid, saying : "If I am differentiated by it, I will have nothing!" The exponential function said calmly: "It can't do anything to me, I am e^x!" The exponential function meets the differential operator. The exponential function introduced itself: "Hello, I am e^x." The differential operator said: "Hello, I am d/dy!"

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