Given that l is the tangent at any point on the image of the function f (x) = 4x / (x ^ 2 + 1), the range of tangent slope is calculated

Given that l is the tangent at any point on the image of the function f (x) = 4x / (x ^ 2 + 1), the range of tangent slope is calculated

The point of the function satisfies the function f (x) = 4x / (x ^ 2 + 1) to obtain the slope of the point. The slope k = f '(x) = (4x / (x ^ 2 + 1))' = [(4x) ′ (x ^ 2 + 1) - 4x (x ^ 2 + 1) ′] / (x ^ 2 + 1) ^ 2 [(U / V) '= (u'v-uv') / V & # 178;] = (4-4x ^ 2) / (x ^ 2 + 1) ^ 2, that is, k = (4-4x ^ 2) / (x ^ 2 + 1) ^ 2

Given that l is the tangent at any point P on the image of the function f (x) = 4x / (x ^ 2 + 1), we can find the range of the slope of L
If f '(x) = - 4 / (x ^ 2 + 1) + 8 / (x ^ 2 + 1) ^ 2, then k = - 4 / (x0 ^ 2 + 1) + 8 / (x0 ^ 2 + 1) ^ 2, let t = 1 / (x0 ^ 2 + 1) ∈ (0,1] How to get (0,1)? The result is? The next process

x0^2>=0、x0^2+1>=1、0

The slope of the curve X ^ 2 = 6y-y ^ 3 at point (- 2,2) is? (how to calculate the slope after derivative)

This is the tangent point
Derivation of X
2x=6*y'-3y²*y'
y'=2x/(6-3y²)
So tangent slope = 2 × (- 2) / (6-3 × 2 & sup2;) = 2 / 3
So it's 2x-3y + 10 = 0

Simple calculation: 2600 ／ 4 ／ 25 2100 ／ 35 25 × 28 370 ／ 5 ／ 2 2600 ／ (26 × 2) 500 × (2 × 27)
Note: when answering, use X or △ instead of * or I can't understand

2600÷4÷25=26×100÷4÷25=26×25÷25=26×1=262100÷35=2100÷7÷5=300÷5=6025×28=25×4×7=100×7=700370÷5÷2=37×10÷5÷2=37×2÷2=37×1=372600÷（26×2）=2600÷26÷2=100÷2=50500×（2×27）=500×2...

Calculation: 4 * 5 + 5 * 6 + 6 * 7 + +25*26+26*27
The calculation process should be clear,

The general term is n (n + 1) multiplied by n ^ 2 + n squared, the sum formula of n terms is s = n (n + 1) (2n + 1) / 6, remove the first three terms, 1 * 2,2 * 3,3 * 4, remove 20, so the result is 26 * (26 + 1) (2 * 26 + 1) / 6 - 20n. The sum formula of 26 * (26 + 1) (2 * 26 + 1) / 6 - 20n is the same as that of S = n (n + 1) / 2, which is (26 * 26 + 1) / 2, but the front side is reduced by 20

Simple calculation of 5 / 27 △ 4 + 22 / 27 × 0.25

5/27÷4+22/27×0.25
=5/27x1/4+22/27×1/4
=(5/27+22/27)x1/4
=1x1/4
=1/4

Simple calculation of 4.5/4-0.35 * 0.25

=4.5/4-0.35/4=9/8-0.7/8=8.3/8=83/80

0.25X0.25X…… X0.25 (99 0.25) x4x4 X4 (100 4) =?

0.25X0.25X…… X0.25 (99 0.25) x4x4 X4 (100 4)
=99 0.25 × 99 4 × 4
=4

(- 5) X4 + 2 / 5 + 7x (- 4 + 2 / 5) - 12) X4 + 2 / 5 + 4 + 2 / 5 = simple calculation method

Simple calculation of 25X (100 + 4)

25x（100＋4）
=25x100+25x4
=2500+100
=2600