The derivative of ( x1/2 ) with respect to 'x' is [ 1/2 x-1/2 ], or 1/[2sqrt(x)] .
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The derivative of cos x is -sin x, the derivative of square root of x is 1/(2 root(x)). Applying the chain rule, the derivative of cos root(x) is -sin x times 1/(2 root(x)), or - sin x / (2 root x).
Yes, because when x equals 1, the square root of x is rational and the square root of -x is irrational, and when x equals -1, the square root of x is irrational and the square root of -x is rational.
The fraction must be rationalized. Since it is the square root of x in the denominator, you are going to multiply the numerator and denominator by the square root of x. For simplicity of the problem, root will take the place of the symbol for square root: root(3y)/root(x) root(3y)*root(x)/root(x)*root(x) root(3xy)/x The simplified answer is going to be the square root of 3xy divided by x. Hope that helped.
It seems to be 25. Call your number "x". x = 5 square root of (5 square root of (5 ...) Square it; this will eliminate the outermost square root sign: x squared = 25 times 5 square root of (5 square root of (... Dividing the second equation by the first one, you get: x squared / x = 25 x / x x = 25
Its the square root of 2 times x Ambiguous. More clear is x times square root of 2