What is (\partial)/(\partial x)(-2sqrt(|x|)) ?

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

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(\partial)/(\partial x)(-2sqrt(|x|))

\frac{\partial}{\partial x} (- 2 ∣ x ∣)

- \frac{x}{∣ x ∣ ∣ x ∣}

Solution steps

\frac{\partial}{\partial x} (- 2 ∣ x ∣)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{x}{∣ x ∣ ∣ x ∣}

y^{^{''}} - 3 y^{^{'}} + 2 y = x^{2}

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\int_{- 1}^{- 2} \frac{16 - x ^{3}}{x ^{3}} d x

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