What is the derivative of |x-1| ?

The derivative of |x-1| is (x-1)/(|x-1|)

What is the first derivative of |x-1| ?

The first derivative of |x-1| is (x-1)/(|x-1|)

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\frac{d}{d x} (∣ x - 1 ∣)

\frac{x - 1}{∣ x - 1 ∣}

Solution steps

\frac{d}{d x} (∣ x - 1 ∣)

Apply the chain rule:

\frac{x - 1}{∣ ( x - 1 ) ∣} \frac{d}{d x} (x - 1)

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

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

= \frac{x - 1}{∣ ( x - 1 ) ∣} \cdot 1

Simplify

= \frac{x - 1}{∣ x - 1 ∣}

(4 y + y x^{2}) d y - (2 x + x y^{2}) d x = 0

x^{2} - x y + y^{2} = 3, (1, 2)

lo g_{2} (x lo g_{5} (x))

y = \frac{2}{sin ( x ) + cos ( x )}, (0, 2)

n = 1 \sum \infty n (0.9)^{n}

What is the derivative of |x-1| ?
The derivative of |x-1| is (x-1)/(|x-1|)
What is the first derivative of |x-1| ?
The first derivative of |x-1| is (x-1)/(|x-1|)