What is the derivative of f(x)=|x-4| ?

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

What is the first derivative of f(x)=|x-4| ?

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

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derivative of

f (x) = ∣ x - 4 ∣

\frac{x - 4}{∣ x - 4 ∣}

Solution steps

\frac{d}{d x} (∣ x - 4 ∣)

Apply the chain rule:

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

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

\frac{d}{d x} (x - 4) = 1

= \frac{x - 4}{∣ ( x - 4 ) ∣} \cdot 1

Simplify

= \frac{x - 4}{∣ x - 4 ∣}

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