What is the derivative of 4-|x| ?

The derivative of 4-|x| is -x/(|x|)

What is the first derivative of 4-|x| ?

The first derivative of 4-|x| is -x/(|x|)

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\frac{d}{d x} (4 - ∣ x ∣)

- \frac{x}{∣ x ∣}

Solution steps

\frac{d}{d x} (4 - ∣ x ∣)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4) - \frac{d}{d x} (∣ x ∣)

\frac{d}{d x} (4) = 0

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

= 0 - \frac{x}{∣ x ∣}

Simplify

= - \frac{x}{∣ x ∣}

What is the derivative of 4-|x| ?
The derivative of 4-|x| is -x/(|x|)
What is the first derivative of 4-|x| ?
The first derivative of 4-|x| is -x/(|x|)