1/sqrt(x^2) - Wolfram|Alpha

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Input

1/sqrt(x^2)

Plot

Plot

Plot

Alternate form assuming x is real

1/abs(x)

Alternate form assuming x>0

1/x

Roots

(no roots exist)

Properties as a real function

Domain

{x element R : x!=0}

Range

{y element R : y>0} (all positive real numbers)

Parity

even

Series expansion at x=0

x/(sqrt(x^2) x) + O(x^9)
(Puiseux series)

Big‐O notation »

Series expansion at x=∞

1/x + O((1/x)^9)
(Laurent series)

Big‐O notation »

Derivative

d/dx(1/sqrt(x^2)) = -x/(x^2)^(3/2)

Indefinite integral

integral1/sqrt(x^2) dx = (x log(x))/sqrt(x^2) + constant
(assuming a complex-valued logarithm)

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