How to find the total differential of Z = Y / (y ^ 2 + x ^ 2) ^ (1 / 2)

How to find the total differential of Z = Y / (y ^ 2 + x ^ 2) ^ (1 / 2)

z=y/(y^2+x^2)^(1/2）z'=-(y/2)2x/(x^2+y^2)^(3/2) = -xy/(x^2+y^2)^(3/2).z'=(x^2+y^2)^(1/2)-y^2/(x^2+y^2)^(1/2)/(x^2+y^2)=x^2/(x^2+y^2)^(3/2).dz=x(-ydx+xdy)/(x^2+y^2)^(3/2)

How to find total differential z = f (x, X / y)

z=f(x,x/y)
∂z/∂x=f1+f2/y
∂z/∂y=-xf2/y^2
dz=[f1+f2/y]dx+[-xf2/y^2]dy

Z = x ^ 3Y ^ 2 + X + y, total differential

dz=d(x³y²+x+y)
dz=（3x²y²+1）dx+（2x³y+1）dy

Let u = Z / √ (x ^ 2 + y ^ 2), find the total differential du (3,4,5)

Partial U / partial x = - XZ / (x ^ 2 + y ^ 2) ^ 3 / 2 = - 3 / 25
Partial U / partial y = - YZ / (x ^ 2 + y ^ 2) ^ 3 / 2 = - 4 / 25
Partial U / partial z = 1 / (x ^ 2 + y ^ 2) ^ 1 / 2 = 1 / 5
Then Du = partial U / partial x * DX + partial U / partial y * dy + partial U / partial Z * DZ
So du (3,4,5) = - 3 / 25dx-4 / 25dy + 1 / 5dz

About resistance, voltage, current, sliding rheostat
In the circuit of measuring the resistance of small bulb, why the higher the voltage is, the higher the resistance will be. Won't the resistance change?

The reason is as follows: first, it has something to do with the principle of the light bulb. After the voltage is applied to the small bulb, there is a current flowing through it. Then the bulb heats up to a certain extent, and the small bulb lights up. Therefore, the incandescent lamps around you are very hot, and only a very small amount of electric energy is converted into light energy, about 30% more, so now the country recommends

-2 √ 5 × (- 1 / 3 √ 15) × √ 4 / 3 Calculation

-2√5×（-1/3√15）×√4/3
=-2√5×(-√15/45)×2√3/3
=4/9;
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RL = 6 Ω, the range of ammeter is 0-0.6a, the range of voltmeter is 0-3v, and the power supply voltage is 9V. In order to make the two meters safe to use
What are the requirements for the resistance of rheostat?

If the RL voltage is 3V, then the current I = u / RL = 3V / 6 Ω = 0.5A, which does not exceed the range of ammeter 0.6A. Then the power supply voltage is 9V, and the extra 6V should be shared by series rheostat, then the rheostat resistance RP = 6V / 0.5A = 12 Ω, that is, the rheostat resistance should be more than 12 Ω

1. It takes the same time for a ship to sail 80 km downstream and 60 km upstream. It is known that the speed of a ship in still water is 21 km per hour,
2. Farmer Zhang Dabo, in order to become rich and well-off, vigorously develops family breeding. He plans to use a 40m long wooden fence to encircle a rectangular sheep pen. In order to save materials and maximize the rectangular area, he uses a 25m long wall of his house to design a rectangular sheep pen as shown in the figure
(1) Please find out the area of Zhang Dabo's rectangular sheepfold
(2) Please judge whether his design is reasonable? If not, how to design? And explain the reason

80 / (21 + x) = 60 / (21-x) = > water velocity x = 3
S=25*7.5=187.5
The unreasonable length and width should be 20m, 10m and the maximum area is 200m ^ 2

All the chemical equations of grade three, the physical equations of grade two and grade three

There are chemical and physical in the attachment;

Life is beautiful because of hard work

Cold, numb, selfish, greedy, like a bayonet, every moment mercilessly stabbing our pure heart; hypocritical, treacherous, see profit forget righteousness, rumors frame up, like a devil cruel