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Popular >

derivative of |2x+1|

Solution

\frac{d}{d x} (∣ 2 x + 1 ∣)

Solution

\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 ∣}

Popular Examples

integral from 1 to 8 of 2/(x^3)

\int_{1}^{8} \frac{2}{x ^{3}} d x

(\partial)/(\partial x)((\sqrt[7]{x})^4)

limit as x approaches 0+of (-ln(x))^x

x \to 0 + lim ((- ln (x))^{x})

derivative of x^2sqrt(x^4-12)

\frac{d}{d x} (x^{2} x^{4} - 12)

(dy)/(dx)=((3x^2))/(y^2)

\frac{d y}{d x} = \frac{( 3 x ^{2} )}{y ^{2}}

Frequently Asked Questions (FAQ)

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|)