What is the derivative of-|x| ?

The derivative of-|x| is -x/(|x|)

What is the first derivative of-|x| ?

The first derivative of-|x| is -x/(|x|)

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\frac{d}{d x} (- ∣ x ∣)

- \frac{x}{∣ x ∣}

Solution steps

\frac{d}{d x} (- ∣ x ∣)

Take the constant out:

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

= - \frac{d}{d x} (∣ x ∣)

Apply the common derivative:

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

= - \frac{x}{∣ x ∣}