Help to answer Thank you, y = (x-1) cosx + 2011 / X for dy / DX | x = 1

Help to answer Thank you, y = (x-1) cosx + 2011 / X for dy / DX | x = 1

y'=cosx-(x-1)sinx-2011x^(-2)
dy/dx | x=1
=cos1-2011

y=-cosx,dy/dx=?

sinx

What is dy / DX = y + cosx

∵ dy / DX = y + cosx = = > dy YDX = cosxdx = = > dy / e ^ x-ydx / e ^ x = cosxdx / e ^ x (e ^ x divided by both ends of the equation) = = > d (Y / e ^ x) = D ((SiNx cosx) / (2e ^ x)) = = > y / e ^ x = D ((SiNx cosx) / (2e ^ x) + C (...)

Given y = x ^ cosx / 2, find dy / DX,

y=x^cosx/2
Take the logarithm of E on both sides
lny=lnx^cosx/2=cosx/2lnx
The derivation on both sides is very good
y'/y=(cosx/2)'lnx+cosx/2(lnx)'
=-sinx/2*lnx *1/2 +cosx/2*1/x
=1/x*cosx/2-1/2*sinx/2 * lnx
therefore
y'=x^cosx/2*(1/x*cosx/2-1/2*sinx/2 * lnx)

General solution of differential equation dy / DX = 2x / Y

dy/dx=2x/y ,
Separate variables, YDY = 2xdx,
Integral on both sides, 1 / 2 * y ^ 2 = x ^ 2 + C,
y^2=2x^2+C

General solution of differential equation y * dy / DX + e ^ (2x + y ^ 2) = 0

y*dy/dx+e^(2x+y^2)=0,
By separating variables, we get - 2ydy / e ^ (y ^) = e ^ (2x) * D (2x),
The integral is 1 / e ^ (y ^) = e ^ (2x) + C,
Take logarithm to get - y ^ = ln [e ^ (2x) + C],
Y = soil √ {- ln [e ^ (2x) + C]}, is the result

Finding the general solution of differential equation dy / DX = e ^ (2x + y) [1 / 2 (e ^ 2x)] + e ^ y = C

dy/dx=e^（2x+y)
That is dy / DX = e ^ (2x) * e ^ y
E ^ (- y) dy = e ^ (2x) DX is obtained by separating variables
The integral on both sides gives - e ^ (- y) = 1 / 2 e ^ (2x) + C1
A conclusion can be drawn by moving items

The general solution (1-2y) DX - (2 + y) dy = 0
Is to find the general solution (1-2y) DX - (2 + x) dy = 0

The variables were separated as follows
Dy / (1-2y) = DX / (2 + x), the integral of both sides is: LNC / 2-1 / 2 * ln (1-2y) = ln (2 + x)
The general solution is: (1-2y) * (2 + x) ^ 2 = C

Finding the general solution of calculus equation x (Y & sup2; - 1) DX + y (X & sup2; - 1) dy = 0

The differential method X (Y \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\#178; y and#178; - x and#178; -

In a circle with a diameter of 8 decimeters, the center angle of the circle is 45 ° and the arc length is 5
Within 5 minutes

8x π x45 ° / 360 ° ≈ 8x3.14x45/360 = 3.14 (decimeter)