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

The answer to (\partial)/(\partial x)(ln(sqrt(x^2))) is 1/(|x|)

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

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

\frac{1}{∣ x ∣}

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{2}} \frac{\partial}{\partial x} (x^{2})

= \frac{1}{x ^{2}} \frac{\partial}{\partial x} (x^{2})

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

= \frac{1}{x ^{2}} \cdot \frac{x}{∣ x ∣}

Simplify

\frac{1}{x ^{2}} \cdot \frac{x}{∣ x ∣} : \frac{1}{∣ x ∣}

= \frac{1}{∣ x ∣}

\frac{\partial}{\partial z} (x z - 5 x^{2} y^{3} z^{4})

\int (\frac{3}{x} - \frac{5}{x ^{6}}) d x

\frac{d y}{d x} = \frac{x ^{3} - x ^{2} + x}{x}

y = tan (x) + \frac{1}{3} tan^{3} (x)

x \to - 3 lim (x^{3} + 4 x^{2} - 7)

What is (\partial)/(\partial x)(ln(sqrt(x^2))) ?
The answer to (\partial)/(\partial x)(ln(sqrt(x^2))) is 1/(|x|)