What is the derivative of |x-4| ?

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

What is the first derivative of |x-4| ?

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

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\frac{d}{d 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 ∣}

\frac{d}{d x} (sin^{3} (x^{2} - 1))

\int \frac{x + arctan ( x )}{1 + x ^{2}} d x

\frac{d}{d x} (x^{a r c s i n (x)})

\frac{d}{d x} (\frac{4 x + 4 1 + x}{x ^{2} - 1})

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

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