Is this formula correct? C is a constant Is integral the same?

Yes, for calculus, constants can be put forward like this

In the calculation of differential substitution, is DX equal to D (x + C)? (C is a constant)
For example, is DX equal to D (x + C)? Because in some differential reductive substitution problems, sinxdx = - dcosx, and in some problems, sinxdx = - DCOS (x + C), can we say DX = D (x + C)? Please explain or prove in detail,

DX = D (x + C). Because D (x + C) = (x + C) 'DX = DX sinxdx = - DCOS (x + C) is wrong. Because - DCOS (x + C) = - [cos (x + C)]'dx = sin (x + C) DX sinxdx = - dcosx is right. For example, sin (x + C) DX = sin (x + C) d (x + C) = - DCOS (x + C)

The definite integral ∫ a f (x) DX is? A. an original function; B. an original function of F (x); c. a family of functions; D. a non negative constant,
Let's choose one of ABCD. The title is definite integral ∫ upper B lower a f (x) DX is
Maybe it means that the definite integral AB is continuous and f (x) DX is a function or constant.
The senior high school gave it back to the teacher.

Select d (if a

Does the constant a in the definition of function differentiation necessarily take the derivative value of a certain point of the function?
In the differential of the function defined in the first volume of Tongji high number, there is a constant a which does not depend on the increment of the independent variable. Later, a was defined as the derivative value of x0. I want to know whether a has other values or other values? Why?

In the differential of the function defined in the first volume of Tongji high number, there is a constant a which does not depend on the increment of the independent variable. Later, a was defined as the derivative value of x0. I want to know whether a can have other values or other values?
No. a can only take the derivative value f '(x0)
According to the definition of differentiability and differentiability, it can be deduced
Differentiable and differentiable

Is there anyone to help solve this differential equation? Y * y '' = a, y is a function of X, a is a constant!
A differential equation, I do not know how to solve, please master help ah! Best give the solution and process, the answer is good, you can add more points!

The solution of Cauchy problem is as follows
Let y '= P, then y' '= PDP / Dy,
The original formula is as follows:
ypdp/dy=A
==>pdp=Ady/y
Points on both sides:
(1/2)p^2=Alny+C1
==>p=±√(2Alny+2C1)
==>y'=±√(2Alny+2C1)
==>dy/±√(2Alny+2C1)=dx
Points, both sides:
∫±1/√(2Alny+2C1)dy=x+C2
It is the solution of the original equation

It is known that y + B is positively proportional to x + A, where a and B are constants
1. Prove that y is a linear function of X
2. If x = 1, y = - 1; X = 2, y = 2, find the value of y when x = 3

1、
Y + B is proportional to x + a
So y + B = K (x + a)
y+b=kx+ka
y=kx+(ka-b)
K and ka-b are constants
So y is a function of degree X
two
Let P = ka-b
Then y = KX + P
x=1,y=k+p=-1
x=2,y=2k+p=2
subtract
2k-k=2+1
k=3
p=-1-k=-4
So y = 3x-4
So x = 3
y=9-4=5

Let f (x) be continuous on [0,1] and greater than 0 in (0,1) and satisfy the differential equation XF '(x) = f (x) + (3 / 2) ax & # 178; (a is a constant). Moreover, the area of the graph represented by the curves y = f (x) and x = 1, y = 0 is 2. When f (x) is solved and the value of a is asked, the volume of the body of revolution obtained by the graph rotating around X axis is the smallest

1) (3 / 2) f '- F / F / x = (3 / 2) and (3 / 2) f-f / X (3 / 2) and (3 / 2) f-f / x = (3 / 2) as (3 / 2) and (3 / 2) as (3 / 2) and (3 / 2) as (3 / 2) as (3 / 2) and (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) and (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) as (3 / 2) and (3 / 2 (3 / 2) and (3 / 2) as (C / 2 + A / 2 / 2 / 2 / A / 2 / 2 / 2 / 2 / 2 = 2 = 2 = 2 = 2, C / 2 = 2 = 2, C / 2 = 2, C = 2, C = 2, C = 2, C = 2, C = (2) π∫ f &# 17

Finding a function satisfying the differential equation f '(x) + XF' (- x) = x

Differential equation f '(x) + XF' (- x) = x ①
It holds for any X. by replacing x with - x, we get
f'(-x)+(-x)f'(x)=-x
Multiply both sides by X, and you'll get
xf'(-x)-x^2f'(x)=-x^2 ②
① - 2
(1+x^2)f'(x)=x+x^2
f'(x)=(x^2+1+x-1)/(1+x^2)=1+x/(x^2+1)-1/(1+x^2)
The integral of X on both sides is obtained
f(x)=x+1/2*ln(x^2+1)-arctanx+c

When a function is not differentiable at a point, how to judge whether the tangent does not exist or the tangent slope does not exist
Y = x ^ 1 / 3 + 1 is not differentiable at x = 0, tangent equation is x = 0, but y = x ^ 1 / 2 + cosx is not differentiable at x = 0, tangent does not exist, why?

There are several important numbers of function derivations. One is the continuity of function, and whether the left and right derivatives of function at a certain point are the same. There is no necessary connection with tangent

Tangent of derivative function
The tangent equation of curve y = x to the third power at point P (2,8) is

y=12x-16
Get the slope from the derivative first

Is this formula correct? C is a constant Is integral the same?