Find the derivative of the implicit function y = y (x) determined by the equation x / y = ln (XY)

Find the derivative of the implicit function y = y (x) determined by the equation x / y = ln (XY)

The two sides are derived from X
(y-xy')/y^2=(y+xy')/(xy)
Just solve y '

Find the derivative dy / DX (1) x ^ 2 + xy = 1 of the function y = f (x) determined by the following equation

Derivation of X on both sides
2x + xy' + y = 0
So y '= (- 2x-y) / X

If the solution of the equation inx-6 + 2x = 0 is x0, the maximum solution of X ≤ x0 is?

Is x an integer?
Let f (x) = lnx-6 + 2x
f(2)=ln2-20
SO 2

What is sin1?

1 is radian, π radian is 180 degrees, then 1 radian is 180 / π degrees
Sin1 is the sine of 1 radian. If a right triangle has an acute angle a, then its opposite side divided by the hypotenuse = Sina

How to solve the equation (36 + x) / (8 + x) = 3

(36+x)/(8+x)=3
(36+x) = 3*(8+x)
36+x = 24+3x
2x=12
x=6
Test of substitution equation
Left = 36 + 6 / 8 + 6 = 42 / 14 = 3 = right
So 6 is the solution of the equation

The second application of one yuan in junior high school
A wood factory produced 500 desks in January this year. Due to poor management, the output in February decreased by 10%. Since March, the management has been strengthened, and the output gradually increased, reaching 648 in April. If the monthly growth rate in March and April is the same, we should seek this growth rate

Suppose the growth rate is X
500*（1-10%）*（1+X）（1+X）=648
X=20%

A (2,3), B (- 3, - 2), C (4,1) are described in the plane rectangular coordinate system, and a line segment is used to connect a, B, C in turn. Can you find its area

c=|AB|=√[(2+3)^2+(2+3)^2]=5√2
b=|AC|=√[(4-2)^2+(1-3)^2]=2√2
a=|BC|=√[(4+3)^2+(1+2)^2]=√58
a^2=b^2+c^2
S=bc/2=5√2*2√2/2=10

It's 7:05. It's 6:30

five past seven
Six thirty or
half past six

The intercept of the line L and the line x-2y-4 = 0 on the Y axis is the same, and the slope of the line x + 2y-6 = 0 is the same

Let L: y = KX + B be a straight line
Deformation x-2y-4 = 0
Y = 0.5x-2, so the intercept on the y-axis is - 2
So B = - 2
Deformation x + 2y-6 = 0
y=-0.5x+3
So the slope is - 0.5
k=-0.5
So the line L: y = - 0.5x-2

Y = (SiNx) ^ 6 + (cosx) ^ 6 = [(SiNx) ^ 2 + (cosx) ^ 2] [(SiNx) ^ 4 - (sinxcosx) ^ 2 + (cosx) ^ 4] how to do this step?

It's using the cubic sum formula
a³+b³=（a+b）（a²-ab+b²）