Find d2x.dx? . d？ I really don't understand the difference between x and x at all. I hope to have a detailed answer.

1, difference time is different.

D2x and dx? It's all differential, and d? X is a quadratic differential.

2. Differential variables are different.

The differential variable of d2x is 2x, dx? Is the differential variable x? ，d？ The differential variable of x is X.

Let's explain the definitions of these three in detail:

Dx stands for the infinitesimal change of X, where D stands for "differential" and is the first letter of "derivative".

Therefore, in the same way, 2x is considered as a whole:

D2x is expressed as an infinitesimal change of 2x, that is, the value of 2x is differential.

dx？ x？ Change an infinitesimal amount, that is, for x? This value is differential.

d？ X represents another differential based on dx, that is, d? x=d(dx).

Extended data:

X is the symbol of differential, which can be divided into one-dimensional differential and multivariate differential.

Definition: let the function y? =? F(x) is defined in an interval, x0 and x0? +? Δ x is in this interval.

If the function δ y? =? f(x0？ +? δ x) f (x0) can be expressed as? δy？ =? aδx0？ +? O (Δ x0), and O (Δ x0) is infinitely less than Δ x, then the function f(x) is differentiable at point x0, and Δ x is called the differential of the function corresponding to the increment of the independent variable Δ x at point x0, which is denoted as dy, that is, dy? =? δx .

Usually the increment of the independent variable x? Δ x is called the differential of the independent variable and written as dx, that is, dx? =? Δ X. So the function y? =? The differential of f(x) can also be written as dy? =? F'(x)dx. The quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function. Therefore, the derivative is also called WeChat business.

Geometric meaning: let Δ x be curve y? =? The increment of m point on f(x) on the abscissa, δy is the increment of m point curve corresponding to δx on the ordinate, and dy is the increment of tangent of m point curve corresponding to δx on the ordinate.

When | Δ x | is small, |Δy-dy | is much smaller than |Δy-dy | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.