What is the derivative of |2x+1| ?

The derivative of |2x+1| is (2(2x+1))/(|2x+1|)

What is the first derivative of |2x+1| ?

The first derivative of |2x+1| is (2(2x+1))/(|2x+1|)

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\frac{d}{d x} (∣ 2 x + 1 ∣)

\frac{2 ( 2 x + 1 )}{∣ 2 x + 1 ∣}

Solution steps

\frac{d}{d x} (∣ 2 x + 1 ∣)

Apply the chain rule:

\frac{2 x + 1}{∣ ( 2 x + 1 ) ∣} \frac{d}{d x} (2 x + 1)

= \frac{2 x + 1}{∣ ( 2 x + 1 ) ∣} \frac{d}{d x} (2 x + 1)

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

= \frac{2 x + 1}{∣ ( 2 x + 1 ) ∣} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ( 2 x + 1 )}{∣ 2 x + 1 ∣}

What is the derivative of |2x+1| ?
The derivative of |2x+1| is (2(2x+1))/(|2x+1|)
What is the first derivative of |2x+1| ?
The first derivative of |2x+1| is (2(2x+1))/(|2x+1|)