Let z = Z (x, y) be the implicit function determined by the equation x ^ 2 + Z ^ 2 = ysin (Z / x), and find the partial derivative of Z to x, y I am a math idiot

Let z = Z (x, y) be the implicit function determined by the equation x ^ 2 + Z ^ 2 = ysin (Z / x), and find the partial derivative of Z to x, y I am a math idiot

1. Derivative of X (the derivative sign is zero, use "￡" instead)
The derivation of X on both sides is as follows:
2x 2z￡z/￡x=-ycos(z/x)/x^2*￡z/￡x:
The results are as follows
￡z/￡x=-2x/[2z ycos(z/x)/x^2]:
2. Derivation of Y
There is a difference between the two sides
2z￡z/￡y=sin(z/x) ycos(z/x)/x*￡z/￡y:
Simplify
￡z/￡y=sin(z/x)/[2z-ycos(z/x)/x]
The answer is for reference only. Note: when seeking partial derivation, we should pay attention to who is seeking partial derivation and whose partial derivation. In this way, it is very easy. If there is something wrong, please let me know and I will deal with it as soon as possible!

According to the different characteristics of logic functions, digital circuits can be divided into - circuits and - circuits

Combinatorial logic
Temporal logic

Divide the nine numbers 39, 45, 49, 56, 60, 70, 78, 84 and 91 into three groups so that the products of the three numbers in each group are equal. How can we divide them?

Solution 39 = 3 × 13
45=3²×5
49=7²
56=2³×7
60=2²×3×5
70=2×5×7
78=2×3×13
84=2²×3×7
91=7×13
∴39×70×84=78×49×60=45×56×91
The numbers of the three groups are 39,70,84 respectively,
49、60、78,
45、56、91.

How many square meters is 1000 cm?
RT

Centimeter is the unit of length and square meter is the unit of area. There is no conversion between them!

Translation of Part B 3a in unit 7 of PEP seventh grade English volume 1

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18.24.36 is the least common multiple short division: 2 × 3 × 3 × 4 × 6?
2|18 24 36
|________
3 |9 12 18
|_______
3 4 6 (how to change this step?)

18=2×3×3；
24=2×2×2×3；
36=2×2×3×3；
So the least common multiple = 2 × 2 × 2 × 3 × 3 = 72;
If you don't understand this question, you can ask,

4 / x equals 0.5

4/x=0.5
4÷x=0.5
0.5x=4
x=4÷0.5
x=8

In RT triangle ABC, angle a is equal to 90 degrees, ad is perpendicular to D, and the square of AB is BD times BC
Can you draw a picture? It's hard to understand out of thin air

Triangle bad is similar to triangle BCA,
So BD / BA = BA / BC
AB = BD times BC

Uncle Zhang has 240 more chickens than ducks. It is known that the number of chickens is six times that of ducks. How many are there in all?

Suppose: there are x ducks and 6x chickens
According to the meaning of the title: 6x -- X = 240
5x=240
x=48
6x=288
A: there are 288 chickens and 48 ducks

Y = √ - X & # 178; + 2x + 3. Find the domain of definition, range of value and monotone interval of function
That's under the root

- X & # 178; + 2x + 3 ≥ 0x & # 178; - 2x-3 ≤ 0-1 ≤ x ≤ 3  the domain is [- 1,3] let t = - X & # 178; + 2x + 3 = - (x-1) &# 178; + 4 ∵ x ∈ [- 1,3]} x = - 1 or 3, when ymax = 1, Tmax = 4, ymax = 2} the function range is [0,2] ∵ t = - (x-1) &# 178; + 4 is a parabola with opening downward ∵ x ∈ [- 1,1