Finding the total differential of the function u = x2 + sin (Y / 3) + e ^ XY

Finding the total differential of the function u = x2 + sin (Y / 3) + e ^ XY

du=(2x+y*exp(x*y))dx+((cos(y/3))/3+x*exp(x*y))dy

1. The total differential of the function u = y ^ (Z / x) Du (Y > 0) = 2. The function y = e ^ (x / 2) is expanded into a power series of X. for the great Xia, help to solve it
1. The total differential du (Y > 0) of function u = y ^ (Z / x)=
2. The expansion of function y = e ^ (x / 2) into power series of X is
Please help me

1 U=y^(z/x)
dU=eU/exdx+eU/eydy+eU/ezdz
Logarithm u first
lnU=z/x*lny
eU/ey=y^(z/x-1)
1/UdU=z*lny*-1/x^2dx
eU/ex=zlny*y^(z/x)*(-1/x^2)
1/UdU=lny/x
=>eU/ez=lny*y^(z/x)/x
The first problem has been solved
EU / ex is the partial derivative of u to x, followed by the partial derivatives of Y and Z respectively
2. X power series of y = e ^ (x / 2)
y=e^x=1+x+x^2/2!+...x^n/n!+.
Replace X / 2 with X
Overall replacement

Know the square of quadratic function y = half x minus 2x + 1 (1) find the coordinates of vertex a of function image and intersection B of Y axis (2)

Y=X²/2-2X+1;
Y=1/2*(X²-4X)+1=1/2*(X-2)²-1;
A(2,-1)
B(0,1)

Under what circumstances can we not directly use the discriminant method to find the range of fractional function

Finding the range of a function is one of the basic requirements of college entrance examination mathematics, and it appears frequently. It is a common method to find the range of a function by discriminant method. But not all functions in the form of quadratic function can be found by discriminant method, and some functions can not be found by discriminant method, In general, when the domain of definition of fractional function is all real numbers, the discriminant method can be used directly

Every two companies participating in a fair signed a contract, and all companies signed a total of 45 contracts, with a total number of companies______ A company attended the fair

According to the meaning of the question, we get 12x (x-1) = 45, x2-x-90 = 0, X1 = 10, X2 = - 9 (rounding off) answer: there are 10 companies participating in the fair. So the answer is 10

The original price of a TV set is 2000 yuan, and now it is sold at a 20% discount. How much is the current price? How much is it cheaper than the original price? (formula) thank you

Current price: 2000 * 80% = 1600 yuan
Cheap: 2000-1600 = 400 yuan
A: the current price is 1600 yuan, but it's 400 yuan cheaper

If the rational number a is 2 and B is 1, find 1 + (a + 1) (B + 1) of AB and 1 + (a + 2004) (B + 2004) of ab

AB 1 + (a + 1) (B + 1) 1 + (a + 2004) (B + 2004) 1
=1/1×2+1/2×3+1/3×4+…… +1/2005×2006
=1-1/2+1/2-1/3+1/3-1/4+…… +1/2005-1/2006
=1-1/2006
=2005/2006

Give examples to illustrate the meaning of the following algebraic expressions:
π A & sup2; - 9 / A & sup2;
（p+q）²-p²
X + y + Z

π A & sup2; - 9 / A & sup2; the remaining area after cutting a small square with side length of a / 3 in a circle with radius a
(P + Q) & sup2; - P & sup2; the remaining area after cutting a small square with side length P from a large square with side length P + Q
The average of X + y + Z, x, y, Z

Why do things that have no use value have no value?

It is the two basic attributes of commodity: commodity is the unity of use value and value, both of which are indispensable; use value is the material bearer of value, without use value, there is no value;

The sum of the numbers in each digit of a three digit number is 17, and the number in the ten digit number is four times of the number in the hundred digit number. If you transpose the number in the hundred digit number and the number in the single digit number, the new number will be 495 larger than the original number. To find the original three digit number, you need to use a quadratic equation

x+y+z=17
y=4z
x+10y+100z+495=100x+10y+z
x=7
y=8
z=2
The original number was 287