What is the first derivative of x/(|x|) ?

The first derivative of x/(|x|) is 0

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derivative of x/(|x|)

\frac{d}{d x} (\frac{x}{∣ x ∣})

0

Solution steps

\frac{d}{d x} (\frac{x}{∣ x ∣})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ∣ x ∣ - \frac{d}{d x} ( ∣ x ∣ ) x}{∣ x ∣ ^{2}}

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot ∣ x ∣ - \frac{x}{∣ x ∣} x}{∣ x ∣ ^{2}} : 0

= 0