If y = in (x + radical 1 + x ^ 2) is known, then dy=

Given y = in [x + √ (1 + X & # 178;)], then dy=
dy={[1+x/√(1+x²)]/[x+√(1+x²)]}dx={[x+√(1+x²)]/[1+x²+x√(1+x²)]}dx

Find y = [in (1-x)] ^ 2 differential

Find y = in & # 178; (1-x) differential
The solution dy = 2 [ln (1-x)] [- 1 / (1-x)] DX = [2 / (x-1)] ln (1-x) DX

Let y = sin2x + cosx, then dy =?

Y=SIN2X+COSX-SINX
t=(cosx-sinx)
tt=1-2cosxsinx=1-sin2x
sin2x=1-tt
Y=1-tt+t＝-(t-1/2)^2+5/4
－√2

Let y = sin2x / X be the square of dy

dy=[(sin2x)'*x²-sin2x*(x²)']/(x²)² dx
=(2x²cos2x-2xsin2x)/x^4 dx
=(2xcos2x-2sin2x)/x³ dx

What is the minimum size of a table for 20 people, the minimum size of a table for 20 people in a hotel box, and the diameter of a round table

Let me tell you a calculation method,
According to the standard of 700mm width per person, 20 people need 20 * 0.7 = 14m, which is the circumference of the round table, and then divided by 3.14 to 4.46M, take the whole number, 4.5m
0.7m refers to the chair with armrest, and the chair without armrest can be calculated as 0.5m

The differential of y = ln square (1 + 2x Square)
In a hurry

=2*[ln(1+2x^2)]*(4x)*[1/(1+2*x^2)]
First differential square, then differential LN, and finally differential what's in LN
=[8xln(1+2x^2)]/(1+2x^2)

A round dining table with a diameter of 1.2m and a height of 8m is paved with a square tablecloth. The four corners of the tablecloth just touch the ground. What is the area of this tablecloth

It's 0.8 meters high
Square diagonal 1.2 + 0.8x2 = 2.8m
A square can be seen as two triangles with 2.8 feet long and 1.4 meters high
Area 1 / 2x2.8x1.4x2 = 3.92m2

Finding the differential of function y = in xsinx

y'=1/(xsinx)*(xsinx)'
=1/(xsinx)*(sinx+xcosx)
dy/dx=1/(xsinx)*(sinx+xcosx)dx

Aunt Li went to the cloth shop to buy 28 meters of red cloth and calico, of which the red cloth was 3 yuan per meter and the calico was 5 yuan per meter. When she calculated the account, the salesman mistakenly counted the red cloth as 5 yuan per meter and the calico was 3 yuan per meter, and finally charged Aunt Li 108 yuan. In this way, did Aunt Li pay more or did the shop lose money? Please explain the reason

Red cloth x rice pattern cloth (28-x) M
5X+3（28-X)=108,X=12
3X+5(28-X)=140-2X=140-24=116
116-108=8
The shop lost eight yuan

In (x ^ 2 + y ^ 2) = x + Y-1 differential

The problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is whether the problem is that the LN (x (x (X & \35\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\) / (

If y = in (x + radical 1 + x ^ 2) is known, then dy=