Let z = e ^ XY cos (XY), find DZ | (0,1)

Let z = e ^ XY cos (XY), find DZ | (0,1)

dZ = эZ/эx *dx + эz/эy*dy
= y*e^(xy)*cos(xy)*dx + e^(xy)*[-ysin(xy)]*dx
+ x*e^(xy)*cos(xy)*dy + e^(xy)*[-xsin(xy)*dy
dZ|(0,1) = 1*e^0*cos0*dx - e^0*y*sin0*dx +0*e^0*cos0*dy - e^0*0*sin0*dy
= dx

How many liters of gas and oil can a small car run for 2 / 3 km with 3 / 25 liters of gasoline? How many kilometers can a car run with 9 / 1000 liters of gasoline?

6 / 726 L, 9 / 80 km

In RT triangle ABC, the bisector of acute angle a intersects with the bisector of the adjacent complementary angle of acute angle B at point D. calculate the degree of angle abd?

Should it be the degree of ∠ ADB?
∠ADB=1/2∠C=45°

Given v = 2XY + 3x, find the analytic function f (z) = u (x, y) + IV (x, y) with V as the imaginary part

（1）
∂v/∂x=2y+3
∂ U / &; X = &; V / &; y = 2x (Cauchy Riemann equation)
f‘(z)=∂u/∂x+i(∂v/∂x)=2x+2iy+3i=2z+3i
F (z) = Z & # 178; + 3iz + C, C = - I is obtained from F (0) = - I
∴f(z)=z²+3iz-i

Fill in the blanks: when a piece of ice with a mass of 100g melts into water, its mass and volume will increase

To keep constant; shrink

The speed of light is several times the speed of sound. How fast are they?
What else can be faster than the two? And how fast is a normal plane?

The speed of light is 300000 kilometers per second
The speed of sound is 340 meters per second
According to Einstein's theory of relativity, it's impossible to go faster than the speed of light,
The speed of an aircraft can exceed the speed of sound, that is, Mach 1-2

Let f (x) = loga (2 ^ - x-1) (a > 0, and a ≠ 1), find the value range of X with F (x) > 0

In the first case, when a > 1, loga (2 ^ - x-1) > 0 pushes out 2 ^ - X-1 > 1 pushes out X

90 ° to 35 ° 42 ′ 52 ″

90°-35°42′52〃
=89°59′60〃-35°42′52〃
=54°17′8〃

Prime numbers within 1-100, composite numbers, odd numbers, even numbers

1 to 100:
1 is neither prime nor composite
Prime numbers (i.e. prime numbers) (only divisible by 1 and itself): 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 (each of the above numbers has only 1 and itself) [a total of 25]
Composite number: (there are non-zero divisors except 1 and itself, that is, they can be divisible by some other non-zero natural number except 1 and itself) 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,71,72,74,75,77,78,80,81,82,84,85,86,88,90,92,93,94,95,96,98,99, 100 [74 in total]
Odd: (odd) 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99 [total 50]
Even number: (even number, which can be divided by 2, actually 0 is even, but you require 1 to 100, 0 is not in its interval) 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98100 [total 50]

Calculate 1 / 1 * 2 * 3 + 1 / 2 * 3 * 4 + 1 / 3 * 4 * 5 +. + 1 / 48 * 49 * 50

1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50 =（1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+…… +1/48*19-1/49*50）÷2=（1/1*2-1/49*50）÷2=（1/2-1/2450）÷2=1/4-1/4900=1224/4900=306/1225