What is the derivative of |x-5| ?

The derivative of |x-5| is (x-5)/(|x-5|)

What is the first derivative of |x-5| ?

The first derivative of |x-5| is (x-5)/(|x-5|)

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\frac{d}{d x} (∣ x - 5 ∣)

\frac{x - 5}{∣ x - 5 ∣}

Solution steps

\frac{d}{d x} (∣ x - 5 ∣)

Apply the chain rule:

\frac{x - 5}{∣ ( x - 5 ) ∣} \frac{d}{d x} (x - 5)

= \frac{x - 5}{∣ ( x - 5 ) ∣} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= \frac{x - 5}{∣ ( x - 5 ) ∣} \cdot 1

Simplify

= \frac{x - 5}{∣ x - 5 ∣}

(- 5.6) (4)

\int \frac{1}{4 x ^{2} - 8 x + 32} d x

\int 1 + 5 x^{3} (15 x^{2}) d x

\int \frac{c _{1}}{x cos ^{2} ( ln ( x ) )} d x

x \to 1 lim (- x + 1)

What is the derivative of |x-5| ?
The derivative of |x-5| is (x-5)/(|x-5|)
What is the first derivative of |x-5| ?
The first derivative of |x-5| is (x-5)/(|x-5|)