Y = a ^ x-a ^ (- x) (a > 0 and a ≠ 1)?

Y = a ^ x-a ^ (- x) (a > 0 and a ≠ 1)?

y‘=（a^x）’+（a^-x）‘
=（a^x）lna-（a^-x）lna
=lna（a^x-a^-x）

Y = a ^ x * B ^ x

y=a^x*b^x =(a^x)'b^x+a^x(b^x)' =a^x lna b^x+a^x b^x lnb =a^x*b^x(lna+lnb)

A rectangular vegetable field has a circumference of 264 meters, and its length is three times of its width. What is the length and width of this vegetable field

Let the width be x meters
2(3x+x)=264
8x=264
x=33
long
33X3 = 99m

Seek the second small question of the first question on page 10 of the sixth grade mathematics Evaluation Handbook (Volume 2, grade 6). (to be published in Jiangsu)
Hurry up! It's urgent!

The problem is as follows: there are four piles of pieces, and the number of pieces in each pile is 1, 9, 9 and 9 respectively. The two people take turns to take pieces, and each time they can only take one, two and three pieces from one pile. They can even take all the pieces from this pile, but they can't do without taking them. In the end, whoever doesn't have any pieces will lose. How can they become the "ever victorious general"?

General solution of [e ^ (x + y) - e ^ x] DX + [e ^ (x + y) - e ^ y] dy = 0

Total differential equation
The general solution is (e ^ x-1) (e ^ Y-1) + C

How many spelling methods are there to make a cuboid with 24 small cubes with a side length of 1cm?
For example: length, width and height
Calculate the surface area,

Because 24 = 1 * 1 * 24 → → the surface area is 51
=1 * 2 * 12 → → the surface area is 76
=1 * 3 * 8 → → the surface area is 70
=1 * 4 * 6 → → the surface area is 68
=2 * 2 * 6 → → the surface area is 56
=2 * 3 * 4 → → the surface area is 52
So there are six

In order to meet the 90th anniversary of the founding of the Communist Party of China, the Municipal Children's palace paints the same eight columns in the hall. The perimeter of the bottom surface of each column is 3.14 meters, the height is 5 meters, and the paint is 0.5 kg per square meter. How many kg of paint do you need?

3.14*5*0.5*8=62.8kg

Using 7, 6, 6 and 8, using the operation symbol and a small bracket, the result is equal to 24
3. 7, 9, 13 a group of 7, 3, 4, 6 a group of 2, 8, 9, 13 a group of the same operation symbol and a small bracket to make the result equal to 24

"2,8,9,13" is 2 times (13 + 8-9)
"3,7,9,13" has 7 times 9-3 times 13
There's nothing left!

General solution of dy / DX + Y / 3 = 1 / 3 (1-2x) y ^ 4

Let z = y ^ (- 3), then y '= (- 1 / 3) Z ^ (- 4 / 3) DZ / DX
By substituting it into the original equation, we can simplify it
dz/dx-z=2x-1.(1)
∵ equation (1) is a first order linear differential equation
The first order linear differential equation is used to solve the equation
Z = CE ^ x-2x-1 (C is the integral constant)
==>y^(-3)=Ce^x-2x-1
==>(Ce^x-2x-1)y³=1
So the general solution of the original equation is (CE ^ x-2x-1) y & # 179; = 1 (C is an integral constant)

The fourth power of the cube of (X-Y) multiplied by the cube of (Y-X) multiplied by the square of the third generation of (X-Y)

[(x-y)^3]^4*(y-x)^3*3(x-y)^2
=(x-y)^12*[-(x-y)^3]*3(x-y)^2
=-3(x-y)^(12+3+2)
=-3(x-y)^17.