What is the derivative of |x-2| ?

The derivative of |x-2| is (x-2)/(|x-2|)

What is the first derivative of |x-2| ?

The first derivative of |x-2| is (x-2)/(|x-2|)

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\frac{d}{d x} (∣ x - 2 ∣)

\frac{x - 2}{∣ x - 2 ∣}

Solution steps

\frac{d}{d x} (∣ x - 2 ∣)

Apply the chain rule:

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

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

\frac{d}{d x} (x - 2) = 1

= \frac{x - 2}{∣ ( x - 2 ) ∣} \cdot 1

Simplify

= \frac{x - 2}{∣ x - 2 ∣}

e^{(\frac{3}{x})}

\frac{d}{d x} ((x^{5} - 7)^{2})

\int \frac{sin ( ln ( x ) )}{x} d x

\int \frac{x ^{2}}{( x ^{2} + 25 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{1}{- x ^{2}})

What is the derivative of |x-2| ?
The derivative of |x-2| is (x-2)/(|x-2|)
What is the first derivative of |x-2| ?
The first derivative of |x-2| is (x-2)/(|x-2|)