What is the derivative of |x-9| ?

The derivative of |x-9| is (x-9)/(|x-9|)

What is the first derivative of |x-9| ?

The first derivative of |x-9| is (x-9)/(|x-9|)

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\frac{d}{d x} (∣ x - 9 ∣)

\frac{x - 9}{∣ x - 9 ∣}

Solution steps

\frac{d}{d x} (∣ x - 9 ∣)

Apply the chain rule:

\frac{x - 9}{∣ ( x - 9 ) ∣} \frac{d}{d x} (x - 9)

= \frac{x - 9}{∣ ( x - 9 ) ∣} \frac{d}{d x} (x - 9)

\frac{d}{d x} (x - 9) = 1

= \frac{x - 9}{∣ ( x - 9 ) ∣} \cdot 1

Simplify

= \frac{x - 9}{∣ x - 9 ∣}

What is the derivative of |x-9| ?
The derivative of |x-9| is (x-9)/(|x-9|)
What is the first derivative of |x-9| ?
The first derivative of |x-9| is (x-9)/(|x-9|)