What is (\partial)/(\partial x)(sqrt(x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2)) is x/(|x|)

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(\partial)/(\partial x)(sqrt(x^2))

\frac{\partial}{\partial x} (x^{2})

\frac{x}{∣ x ∣}

Solution steps

\frac{\partial}{\partial x} (x^{2})

Apply radical rule:

a^{2} = ∣ a ∣

= \frac{\partial}{\partial x} (∣ x ∣)

Apply the common derivative:

\frac{\partial}{\partial x} (∣ x ∣) = \frac{x}{∣ x ∣}

= \frac{x}{∣ x ∣}

What is (\partial)/(\partial x)(sqrt(x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2)) is x/(|x|)