![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Why are the mixed partial derivatives of functions of two variables equal when they are continuous? Don't say that's what the textbook says
We can see from the form that DZ / DX / dy = DZ / dy / DX
Personal opinions and general feelings should be equal
The partial derivative of binary function is greater than zero
Such a function f (a, b) = 2Ab / (a + b), where a, b > 0, and the domain is an ellipse a ^ 2 + 4B ^ 2 = 1 in the first quadrant. Find its maximum
Two partial derivatives are always greater than zero, how to find. I consider that it increases in the direction of a and B, but I don't know which point is the smallest, because the two elements in the domain of definition are reciprocal
If it is a similar problem, there will be a general method
In addition, the wrong number is f (a, b) = 2Ab / (a + 2b). The answer to this question is two-quarters root sign, zz19910622 is right
f(a,b)=2ab/(a+b)
Condition a & sup2; + 4B & sup2; - 1 = 0
L=[2ab/(a+b)]+λ(a²+4b²-1)
L'(a)=[2b²/(a+b)²]+2λa=0
L'(b)=[2a²/(a+b)²]+8λb=0
Solve two algebraic expressions of λ, and then they are equal
a³=4b³
Combined with a & sup2; + 4B & sup2; - 1 = 0, the values of a and B are solved
Higher number: in binary function, there is a conclusion: the extreme point with partial derivative must be a stationary point, but the stationary point is not necessarily an extreme point
Higher number: there is a conclusion in binary function: "the extreme point with partial derivative must be a stationary point, but the stationary point is not necessarily an extreme point."
What I want to ask is: is there such a conclusion in univariate function: "the extreme point with derivative must be a stationary point, but the stationary point is not necessarily an extreme point"?
There is such a conclusion in the function of one variable
Is partial derivative only a concept in binary function? Is it not suitable for functions of three variables or above?
Partial derivative is the concept of functions of more than two variables. Similar definitions can be used for functions of three variables or more variables
Hope to help you, if you solve the problem, please click the "select as satisfactory answer" button below
Some questions about multivariate functions and partial derivatives. (involving compound functions) (higher numbers)
If f (x + AZ, y + BZ) = 0 and f (&) is differentiable, then a (δ Z / δ x) + B (δ Z / δ y) =
Find the solution to the problem
PS: as for the function in the question, is Z the compound of X and y when we seek the derivative of X?
(some of the principles are related to the previous question: 'Q: finding partial derivatives of multivariate composite functions, some other problems! (higher numbers)')
Maybe I didn't express my question very clearly, but I feel more and more clear
It is understood that by the 3-variable equation f (x + AZ, y + BZ) = 0 of X, y, Z is the binary function of X, Y: z = Z (x, y) [this belongs to the case of implicit function] and the function f (x + AZ, y + BZ) on the left of equation f (x + AZ, y + BZ) = 0 is the form of composite function [this belongs to the case of composite function]
The difference between derivative and differential
For a function of one variable y = f (x), there is no difference between derivative and differential. The geometric meaning of derivative is the instantaneous rate of change of curve y = f (x), that is, the tangent slope. Differential is the ratio of increment of dependent variable to increment of independent variable △ y =
Is differentiation the derivation?
Almost
Seeking derivative or differential
1. Y = x ^ 10-10 ^ x + e ^ 3, find y '
2. Y = arctan (1 / x), find dy
3. Y = LNX, find dy
4. Y = xlnx, find y ″
5. Let x ^ 3 + x ^ 2 · y + y ^ 2 = 1, find dy / DX
1.y'=10x^9-10^xln10 2.dy=-dx/1+x^2 3.dy=dx/x*lnx*lnlnx 4.y'=lnx+1 y''=1/x 5.3x^2+2xy+x^2*dy/dx+2y*dy/dx=0 dy/dx=-（3x^2+2xy)/(x^2+2y)
Derivative differential
TGA = (Y-Y1) / (x-x1)?
The function expression should be:
y=（x+x1）tgA+y1
Where x1, Y1 and a are all constants,
Then it's easy to find the differential of Y over X
dy=tgA*dx
Differential and derivative problems
What's the difference between Y 'and Dy
Y 'is the derivative of y to a variable and Dy is the differential of Y
For example, y is derived from X, y '= dy / DX, Dy = y'dx
RELATED INFORMATIONS
- 1. Differential derivative speed Differential derivation What is (f ^ - 1) 'equal to?
- 2. What is the principle of increasing and decreasing functions?
- 3. The proof of the limit of higher number lim n^(1/n)=1 How to prove it?
- 4. There is another problem: for indefinite integral, the integrand is 1 / (1 + x ^ 4) thank you
- 5. How to find the original function of integrand in indefinite integral F '(x) = f (x), given f (x), how to find f (x)
- 6. If the marginal income function is known, the income function can be obtained A detailed explanation of the question is helpful for the respondent to give an accurate answer
- 7. The definition of bounded function If | f (x)|
- 8. Why is a function defined on a closed interval and monotone, then it must be integrable? What are the necessary conditions for monotonicity?
- 9. If a function is bounded on a closed interval, but there are infinite discontinuities, is the function necessarily not integrable? If it is integrable, what conditions should it satisfy
- 10. Can you specify how to prove that a function is continuous and differentiable in a certain (open and closed) interval? I already know the continuity and differentiability at a certain point! Search a lot of answers, feel only said in a certain point, or did not say clearly! Like the following topic! In the first step, how do you know that it is differentiable and continuous in the interval of real number axis? It is not necessary to find out the derivative of the function f (x) = (x-1) (X-2) (x-3) (x-4) (X-5). It is shown that the equation F & # 61602; (x) = 0 has several real roots, and the interval in which they are located is pointed out. Because the function f (x) = (x-1) (X-2) (x-3) (x-4) (X-5) is continuous and differentiable on the whole real axis, and f (1) = f (2) = f (3) = f (4) = f (5) = 0, applying Rolle's theorem in the interval (1,2), (2,3), (3,4), (4,5) respectively, we can obtain that the equation F &; (x) = 0 has at least four real roots, but because F &; (x) is a polynomial of degree 4, there are at most four real roots, so the equation F &; (x) has four real roots; (x) = 0 has only four real roots and is located in the interval (1,2), (2,3), (3,4), (4,5) respectively
- 11. On the differential operator method The operator method is used to find the special solution, For example, y * = {1 / (1 + 2D + D ^ 2)} (x ^ 2 + X + 1) The question is how to get the quotient of D from 1 / (1 + 2D + D ^ 2) Hope to list the detailed division steps The first floor uses Taylor expansion to find the quotient? What if P (d) = 1 + D + D ^ 2
- 12. Solving the ordinary differential equation y + 2XY '+ (x ^ 2) y' ', etc Er, it's y + 2XY '+ (x ^ 2) y' '= 0
- 13. The general solution of the second derivative of differential equation y - the first derivative of 4Y + 4Y = e ^ 2x + X
- 14. The general solution of Y '' + 2Y '+ 10Y = 0 differential equation
- 15. Let F X = e Λ x-k / 2x Λ 2-x 1, if k = 0, find the minimum value of F X 2, if x ≥ 0 Let F X = e Λ x-k / 2x Λ 2-x If k = 0, find the minimum value of FX 2 if FX ≥ 1 when x ≥ 0, find the value range of real number K
- 16. When x ∈ [0,1], find the minimum value of the function f (x) = x & sup2; + (2-6a) x + 3A & sup2
- 17. The function y = f (x) is an even function on (- ∞, + ∞). When x ≥ 0, f (x) = x ^ 2-2x-3. The expression of y = f (x) is written in the form of piecewise function There should be a process
- 18. |What is the geometric meaning of X | and | x-a | ± | X-B |? As the title, as the title
- 19. The significance of gradient Grad = AI + BJ in gradient What kind of quantity is grad? Is it the rate of change on the z-axis? What is the corresponding relationship? Whenever X-axis changes a, Y-axis changes B, z-axis changes grad? Grad should be in the XY plane
- 20. Teacher, I would like to ask you about the slope of derivative. The minimum tangent of slope is parallel to 12x + y = 6. Then the calculation process of the slope of the tangent is detailed