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y=x^(1/2)
y'=1/2*x^(1/2-1)
=1/2*x^(-1/2)
=1 / (2 * root x)

How to calculate the root sign x under the root sign, that is, 1 / 2 and 1 / 2

Let me give you an example
Square root 16, that is, to the power of (1 / 2 of 16) to the power of 1 / 2
Just multiply two half's
To the 1 / 4 power of 16 is 16 to the power of 4

How to calculate the root three X + x = 1000? I'm not smart,

√3x+x=1000
(√3+1)x=1000
x=1000/(√3+1)
=1000(√3-1)/(√3+1)(√3-1)
=500(√3-1)
=500√3-500

How to calculate (x ^ 2 + 1) under the integral root sign?

This thing is very troublesome. Please read it patiently
Let I = ∫√ (x 2 + 1) DX
Then I = x √ (x? 2 + 1) -∫ XD [√ (x? 2 + 1)]
=x√(x²+1)-∫[x²/√(x²+1)]dx
=x√(x²+1)-∫[(x²+1)/√(x²+1)]dx+∫[1/√(x²+1)]dx
=x√(x²+1)-I+∫[1/√(x²+1)]dx
∴I=(1/2){x√(x²+1)+∫[1/√(x²+1)]dx}
Find ∫ [1 / √ (x? + 1)] DX:
Let x = tant, then √ (x? 2 + 1) = sect, DX = sec? TDT
∫[1/√(x²+1)]dx
=∫sec²t/sect dt
=∫sect dt
=ln|tant+sect|+C
=ln|x+√(x²+1)|+C
∴I=(1/2){x√(x²+1)+∫[1/√(x²+1)]dx}
=(1/2)[x√(x²+1)+ln|x+√(x²+1)|]+C
C is an arbitrary constant

How to calculate the root two / 2 = 2 ^ a

2^a=2^(1/2)/2
=2^(1/2-1)
=2^(-1/2)
a=-1/2

Calculation: (2 times root 5-root 3) ^ 2 - (5 times root 2 + root 3) ^ 2

(2 times root 5-root 3) ^ 2 - (5 times root 2 + root 3) ^ 2
=(2√5)²-2×2√5×√3+(√3)²-(5√2)²-2×5√2×√3-(√3)²
=20-4√15-50-10√6
=-30-4√15-10√6

(x-2-x + 12 of 2) divided by X + 4-x of 2, where x = - 4 + radical 3 should be simplified first and then evaluated

The estimation question should be like this [(X-2) - 12 / (x + 2)] / (4-x) / (x + 2)
=[(X-2)(X+2)/(X+2)-12/(X+2)]*(X+2)/(4-X)
=(X-4)(X+4)/(4-X)
=(X-4)(X+4)/-(X-4)
=-X-4 x = - 4 + radical 3
-X-4 = - (- 4 + radical 3) - 4 = 4-radical 3-4 = - radical 3

First simplify and then evaluate: X-2 3-x ^ (x + 2 - (X-2 / 5), where x = 2 times the root sign 2

The original formula = ((3-x) / (X-2)) / (x + 2-5 / (X-2))
=((3-x) / (X-2)) / ((x ^ 2-9) / (X-2)) (divide the latter part)
=(3-x) / (x ^ 2-9) (approximate)
=(3-x) / ((x + 3) * (x-3)) (denominator factorization)
=-1 / (x + 3) (approximate)
=2-2 times root sign (substituting X and rationalizing denominator)

First simplify and then evaluate (X-2 / x-1) / [(x + 1) - (3 / x-1)], where x = (radical 3) - 2

When x = √ 3-2
Original formula = 1 / √ 3 = √ 3 / 3

X = (root number 2008-2a + root sign a-1004) + 5, simplify root sign x + 1-radical sign x / root sign x + 1 + root sign x + 1 + root sign x + 1 + root sign x / root sign x + 1-radical sign x, and evaluate A is a real number

X = root number (2008-2a) root sign (a-1004) 5
According to the definition domain: 2008-2a > = 0 and a-1004 > = 0
one thousand and four