4 - (square of x) under the root sign is the derivative of a function. How to find this function

4 - (square of x) under the root sign is the derivative of a function. How to find this function

x=2sina
dx=2cosada
Original formula = ∫ 2cosa * 2cosada
=∫(cos2a+1)d2a
=sin2a+2a+C
=2sinacosa+2a+C
=x*√(1-x ²/ 4)+2arcsin(x/2)+C

The discriminant function. X part SiNx. X is less than 1 minus x square XD under the zero root sign The SiNx. X of the discriminant function. X is less than zero 1 minus x squared x under the root sign is greater than or equal to zero

f(x)=sinx/x x=0
When x tends to 0 -, limf (x) = 1
When x tends to 0 +, limf (x) = 0
The left limit is not equal to the right limit,
Therefore, it is intermittent

The parity of the judgment function f (x) = [under the root sign (1 + x ^ 2 + x-1)] / ((1 + x ^ 2 + X + 1))

First judge whether f (x) is 0 when x = 0. If it is not 0, it is not an odd function (which can be used in multiple-choice elimination), and then judge its parity according to the routine. Step 1: F (0) = 0, step 2: F (x) = [(1 + x ^ 2) ^ (1 / 2) + X-1] / [(1 + x ^ 2) ^ (1 / 2) + X + 1] = [(1 + x ^ 2) ^ (1 / 2) + X-1] * [(1 + x ^ 2) ^ (1 / 2) - X-1

The parity of the judgment function f (x) = [under the root sign (1-x ^ 2)] / (|x + 2| + 2)

F (x) = [under the root sign (1-x ^ 2)] / (|x + 2| + 2)
1-x^2≥0
-1 ≤ x ≤ 1, then x + 2 > 0
F (x) = [under the root sign (1-x ^ 2)] / (|x + 2| + 2)
=[under the root sign (1-x ^ 2)] / (x + 4 is a non odd non even function)
If f (x) = [under the root sign (1-x ^ 2)] / (|x + 2| - 2) is an odd function

Judgment function f (x) = (x-1) * under the root sign [(x + 1) / (1-x)] (- 1)

-1

Let the function z = xyln (XY), find the total differential DZ

DZ = [Yin (XY) + y] DX + [Xin (XY) + x] dy separate derivation