If f (x, y) = Xe ^ y, find DF (x, y) │ (0,1)

If f (x, y) = Xe ^ y, find DF (x, y) │ (0,1)

df(x,y)=df(x)+df(y)=e^y+xe^y=e

Let D: x ^ 2 + y ^ 2 ≤ a ^ 2, f (x, y) be a continuous function on D, and f (x, y) = √ (a ^ 2-x ^ 2-y ^ 2) + ∫ ∫ DF (U, V) dudv, find f (x, y)

First of all, we should know that the result of double integral of binary function on domain D is a number (not a function), so we can set ∫ ∫ f (U, V) dudv = a, and double integral domain D on both sides of the equation f (x, y) = (a ^ 2-x ^ 2-y ^ 2) ^ (1 / 2) + A, then we can have ∫ ∫ f (x, y) DXDY = ∫ (a ^ 2-x ^ 2-y ^ 2) ^ (1 / 2) DXDY + ∫

Let the function y = f (x) and the function x = y + arctany be reciprocal functions, and find DF x = 0

F (x) and function x = y + arctany are reciprocal functions
So f (x) = y = x + arctanx
So y '= 1 + 1 / (1 + x ^ 2) = (x ^ 2 + 2) / (x ^ 2 + 1)
So DF (x) = [(x ^ 2 + 2) / (x ^ 2 + 1)] DX

It takes 40 minutes for Party A to process 3 parts and 30 minutes for Party B to process 4 parts. The work efficiency ratio of Party A and Party B is ()

The efficiency of a is 3 / 40, the efficiency of B is 4 / 30, the ratio of the two is efficiency divided, the result is 9 / 16

x-｛3y+[5x-3(x-2y)-5y]-7x｝
Simplification

If it's a combination of similar items, the result is 6x-4y

There are 14 million kg of grain in the three warehouses. The ratio of grain quality in warehouse A and warehouse B is 3:4, and the grain quality in warehouse B and warehouse C is 3:4
The ratio is 6: how many kilos of grain are there in three warehouses?

First, set the value of bank B as 4x, then the value of bank a as 3x. You can know that bank C is 1400-7x, and then calculate the ratio as 4x / 1400-7x. Next, you can solve the unknown number X. maybe you have no condition for this problem, and you can't work out the result. Is there any other condition

The solution of 3.5-x = 7x + 0.5
Please

Mathematics problem 4 and 2 / 3 + [8.6 - (+ 3 and 2 / 3) + (- 7 / 5)] + (- 2 and 3 / 5)
Four and two thirds + [8.6 - (+ three and two thirds) + (- seven fifths)] + (- two and three fifths) process

Remove the brackets
=Four and two thirds + [8 and three fifths - three and two thirds - seven fifths] - 2 and three fifths
=Four and two thirds + eight and three fifths - three and two thirds - seven fifths - two and three fifths
=Four and two thirds + eight and three fifths - three and two thirds - one and two fifths - two and three fifths
=7 - two fifths
=Six and three fifths

Let Sn be the sum of the first n terms of an equal ratio sequence and 3s3 = a4-2, S2 = a3-2, then q is the common ratio=

It is known that 3s3 = a4-2
3S2=a3-2.②
①-②.3a3=a4-a3
4a3=a4
Let the common ratio be Q
4a3=a3q
∴q=4

Simple operation of 12 times 199

12x199
=12x(200-1)
=12x200-12x1
=2400-12
=2388